The Rockies also will receive $2 million from the A's to help offset Anderson's salary, a source told ESPN's Buster Olney.
Anderson, who was the Opening Day starter for the A's last season, is due to make $8 million in 2014 and has a $12 million contract option for the 2015 season. That includes a $1.5 million buyout.
"Thanks to the A's Organization and Fans for everything," Anderson posted on Twitter. "I'll nothing but fond memories of my time there."
Of his move to Denver, he added: "Peyton Manning and I are going to become best friends...fact."
Anderson went 1-4 with a 6.04 ERA in five starts and 16 appearances, finishing up as a reliever in an injury-interrupted season.
He returned in the summer of 2012 after missing 14 months following Tommy John surgery. During his lengthy rehab, Anderson worked to improve his fitness and lost more than 20 pounds. He then missed four months this past season with a sprained right ankle and stress fracture in his right foot.
"Great talent and certainly moments of brilliance," A's general manager Billy Beane said of the 25-year-old Anderson at the winter meetings. "From the Rockies' end, they're probably getting him at a great time. He's been through the Tommy John. He's always been motivated. He's a hard worker, and this is the time to get him, because the cost of acquisition a couple of years ago on Brett, well there really wasn't one. He was an untouchable."
The power-armed Pomeranz was on the disabled list late in the season with left biceps tendinitis. He went 0-4 with a 6.23 ERA in eight outings (four starts) and 21 2/3 innings. He went 2-9 in 22 starts the previous year. Beane said he envisions keeping him as a starter but eventually could work him into a bullpen role.
"We had a lot of starting pitching, and in the acquisition of Pomeranz, it allows us to turn back the clock a little with another very talented left-hander," Beane said. "Brett's been with us for several years, and someone obviously with that kind of talent we think very highly of, but with the amount of guys we have, we knew we could use that to get younger guys with less service time, and that was attractive."
Jensen went 5-8 with a 4.55 ERA in 152 1/3 innings for Class A Modesto. He had 136 strikeouts and 39 walks in 28 starts.
The Associated Press contributed to this report.