On Dec. 20, a source told ESPN that the deal is for $52 million. The deal includes an $8 million signing bonus with annual salaries of $11 million per year, according to a Cubs source.
"You look at the (Cubs) on paper, and there's a lot of potential there," Jackson said. "I've been on a lot of teams that you look on paper and no one expects you do to do anything, and you make it to the World Series or go to the playoffs.
"It's definitely one of those teams where you're a few pieces from being where you want to be. I feel like with the additions we have and the team we have right now, we can go out and win ball games and have fun."
Jackson, 29, was 10-11 with a 4.03 ERA in 31 starts (189 2/3 innings) with the Washington Nationals in 2012. He has a 70-71 career record with a 4.40 ERA. In 2012, Jackson had 168 strikeouts and 58 walks but also gave up 23 home runs.
After going 12-9 with a 3.79 ERA in 199 2/3 innings for the Chicago White Sox and St. Louis Cardinals in 2011, Jackson wasn't able to get a long-term deal, and signed a one-year contract for $11 million with the Nationals.
Jackson has played for seven teams in his career, which began with the Dodgers in 2003. The 2010 season included his 150-pitch no-hitter with the Arizona Diamondbacks.
"I think the most assuring part is you have a chance to relax and have a chance to know you're going to be somewhere for a while, and you don't have to feel like you have to prove yourself every year," Jackson said of his new deal. "I feel like it's definitely going to help for myself just to go out and have fun and not worry about anything else."
Jackson joins a Cubs rotation that now includes free-agent additions Scott Baker and Scott Feldman, along with holdovers Matt Garza, Jeff Samardzija and Travis Wood. The Cubs added another starting option in right-hander Carlos Villanueva, who agreed to a two-year contract last month, a major league source told ESPNChicago.com's Bruce Levine.
"I think you're never happy with your depth, but we certainly worked really hard to build it up," Cubs general manager Jed Hoyer said. "That was a big factor for us. We felt like what we were running out there in September once we traded a couple guys, once we shut Samardzija down, it wasn't the quality we were looking for.
"We needed to really address our depth. We've worked hard it. We'll find out over the course of six months whether we were right or wrong about it. ... That was sort of our goal this winter to add as much depth and quality as we could."
Villanueva, 29, was 7-7 with a 4.16 ERA in 38 appearances with the Toronto Blue Jays in 2012, including 16 starts.
Scott Powers contributed to this report.