The Police Ombudsman launched an inquiry after a complaint was made that police did not fully investigated claims against the Sinn FÃ©in president.
A police probe into the allegations was conducted properly, it said.
The ombudsman, Dr Michael Maguire, said there were no signs of misconduct.
He also said he had "found no evidence to indicate that [police officers'] thinking was influenced by who Mr Adams was".
The complaint was in relation to Mr Adams' evidence in the case of his brother, Liam.
Liam Adams was convicted in 2013 of raping his daughter, Ã
A recommendation not to prosecute Gerry Adams over allegations he withheld information on sexual abuse within his family was not politically motivated, a police watchdog has found.