Jones, 29, who became an unrestricted free agent Friday, played 27 games with the Oilers in 2012-13, scoring two goals and finishing with seven points. In the two prior seasons, he scored a career-high 18 goals in 2010-11 and had 17 goals and a career-best 33 points in 2011-12.
"I'm really excited. It's no secret that I love being in Edmonton and love playing for Edmonton," Jones told the Oilers website. "Going into this free agency, our main priority was to get a deal done back with Edmonton and I'm extremely happy and glad to have got that done."
His 2012-13 season ended in late December when he sustained an eye injury.
"I left a little bit to be a desired last year and I wanted to come back and redeem myself and prove to people that I still have a ton of game left in me," Jones said.
"The eye injury left me a little bit tentative on the ice and that's not a game that I can play," he added. "I need to become a menace when I'm out there, be hard to play against, always be around the net and just be a guy that when the other team leaves the ice they don't enjoy when you're out there.
Jones, who was claimed by the Oilers on waivers from the Nashville Predators on April 3, 2010, has 52 goals and 94 points in 282 regular-season games with the Predators and Oilers.
Bachman, 25, played 13 games for the Dallas Stars in 2012-13 and had a 6-5-0 record with a 3.25 goals-against average and .885 save percentage. He also played six games for the Texas Stars in the American Hockey League, where he was 5-1-0 with a 2.31 GAA and .920 save percentage.
In 32 NHL games, Bachman has a 14-10-1 record with a 2.94 goals-against average and .901 save percentage.
The 5-foot-10, 175-pound native of Salt Lake City was Dallas' fourth-round choice (No. 120) in the 2006 NHL Draft.