Oliver signed a one-year contract with the Jets on Sunday, Rich Cimini of ESPN.com reports.
The 49ers released Oliver on Friday, Matt Maiocco of NBC Sports Bay Area reports.
Oliver appeared in 17 regular-season games with San Francisco in 2023, finishing with 67 tackles (48 solo), two passes defended and one interception.
Oliver had 10 tackles (seven solo) in Sunday's 31-17 loss to the 49ers.
49ers defensive coordinator Steven Wilks said Friday that Oliver is expected to play nickelback in 2023, David Lombardi of The Athletic reports.
Oliver recorded nine tackles (five solo), two pass defenses and one sack during Sunday's 20-19 win over Arizona.
Atlanta activated Oliver (knee) from its injured reserve list Saturday ahead of Sunday's game versus San Francisco, Michael Rothstein of ESPN.com reports.
Oliver (knee) was designated to return from injured reserve and practiced Wednesday, Scott Bair of the Falcons' official site reports.
The Falcons placed Oliver (knee) on injured reserve Thursday, Josh Kendall of The Athletic reports.
Oliver (knee) practiced with Atlanta's first-team defense during 11-on-11 drills Friday, Ashton Edmunds of the team's official site reports.