A de-classified report made available by the CIA does show testing by elements of the U.S. government into paranormal perception and testing of Uri Geller. However, these experiments were not conducted by the CIA and the project was scrapped in 1995 after a CIA report concluded that it was never useful in any intelligence operation.
The source that these news articles, and many others like it, use is a declassified CIA report from 4-11 August 1973 labeled "APPENDIX I, EXPERIMENTS - URI GELLER AT SRI".
From the "Objective" section in the report:
The objective of this group of experimental sessions was to verify Geller's apparent paranormal perception under carefully controlled conditions with the goal of understanding the physical and psychological variables underlying such ability
From the "Experimental Program" section in the report:
In each of the eight days of this experimental period picture-drawing experiments were carried out. In these experiments Geller was separated from the target material either by an electrically isolated shielded room or by the isolation provided by having the targets drawn on the East Coast. As a result of Geller's success in this experimental period, we consider that he has demonstrated his paranormal perceptual ability in a convincing and unambiguous manner.
The report continues by detailing some of the experiments that were carried out over a period of eight days in August 1973. Some of the experiments show confirmations in remote viewing, while others are failures.
[...] The first word obtained in this manner was "fuse" and the object drawn was a firecracker. [...] His almost immediate response was that he saw "a cylinder with noise coming out of it". [...] His drawing representing his response to the target was a drum, along with a number of other cylindrical-looking objects.
The target selected from the dictionary was an outline drawing of a man, which evolved through the drawing process into a devil with a trident. [...] Geller spent almost a half-hour working on the drawing before "passing", as he felt unable to get the drawing. [...] The inability on Geller's part to draw the devil may be culturally induced.
A picture was drawn by a scientist outside of the usual experimental group. [...] He drew a number of pictures, all of which he rejected as not being applicable. He said that he got no clear impression and passed. The target was a rabbit, and nothing Geller drew in any way resembled a rabbit. It should be added that the picture was drawn by a scientist of whom Geller is not fond, and Geller asked at the outset if this was the case.
The two target pictures were a tree and an envelope. He experienced difficulty, did not make a drawing that corresponded to either drawing, and passed. Also, he found it very difficult to hold adequately still to make good EEG records. The same skeptical experimenter who drew the rabbit was the EEG operator on this second unsuccessful day.
Of particular note is the presence of this "skeptical experimenter" who Geller was allegedly not fond of. Later in the report, on 8 August, the report remarks
Good results were obtained on the four days when there was no openly skeptical observer.
This report, along with numerous others, were released as part of a declassification of PROJECT STARGATE, described on Wikipedia as
[...] primarily involved remote viewing, the purported ability to psychically "see" events, sites, or information from a great distance.
Of note is that this was operated by the Defense Intelligence Agency and SRI International, not by the Central Intelligence Agency as is often attributed in news articles and stories about Mr. Geller.
PROJECT STARGATE was transferred from the DIA to the CIA in 1995 as part of the defense appropriations bill. A report commissioned by the CIA by the American Institutes for Research found that remote viewing had never been established by the tests, and that remote viewing had never been used operationally. After this report, the CIA cancelled and declassified the program.
The report led to the following conclusions
The conditions under which the remote viewing phenomenon is observed in laboratory settings do not apply in intelligence gathering situations. For example,viewers cannot be provided with feedback and targets may not display the characteristics needed to produce hits
The end users indicating that, although some accuracy was observed with regard to broad background characteristics, the remote viewing reports failed to produce the concrete, specific information valued in intelligence gathering
The information provided was inconsistent, inaccurate with regard to specifics, and required substantial subjective interpretation.
In no case had the information provided ever been used to guide intelligence operations. Thus, Remote viewing failed to produce actionable intelligence.
The foregoing observations provide a compelling argument against continuation of the program within the intelligence community. Even though a statistically significant effect has been observed in the laboratory, it remains unclear whether the existence of a paranormal phenomenon,remote viewing, has been demonstrated. The laboratory studies do not provide evidence regarding the origins or nature of the phenomenon, assuming it exists, nor do they address an important methodological issue of inter-judge reliability.
Further, even if it could be demonstrated unequivocally that a paranormal phenomenon occurs under the conditions present in the laboratory paradigm, these conditions have limited applicability and utility for intelligence gathering operations. For example, the nature of the remote viewing targets are vastly dissimilar, as are the specific tasks required of the remote viewers. Most importantly, the information provided by remote viewing is vague and ambiguous,making it difficult, if not impossible, for the technique to yield information of sufficient quality and accuracy of information for actionable intelligence. Thus, we conclude that continued use of remote viewing in intelligence gathering operations is not warranted.
Wikipedia cites David Marks and his book The Psychology of the Psychic as having further issues with the program.
Marks wrote that there were six negative design features of the experiments. The possibility of cues or sensory leakage was not ruled out, no independent replication, some of the experiments were conducted in secret making peer-review impossible. Marks noted that the judge Edwin May was also the principal investigator for the project and this was problematic making huge conflict of interest with collusion, cuing and fraud being possible.
(Note that the Edwin May referred to is almost certainly Dr. Edwin C. May, a member of the Parapsychological Association.)