Two-time AL West champion Oakland had been looking to move Anderson, who is due to make $8 million this season and has a $12 million contract option for the 2015 season. That includes a $1.5 million buyout.
The 25-year-old Anderson was the Athletics' starter on opening day this year. He went 1-4 with a 6.04 in five starts and 16 appearances, finishing up as a reliever in an injury-interrupted season.
''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.''
This marked A's general manager Billy Beane's fourth trade in just over a week.
''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 at the winter meetings in Lake Buena Vista, Fla. ''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.''
Anderson, a second-round draft pick by Arizona in 2006, has been plagued by injuries in recent years.
He returned in the summer of 2012 after missing 14 months following Tommy John elbow 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,'' Beane said. ''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 with four starts and eight outings for 21 2-3 innings. He went 2-9 in 22 starts the previous year. Beane envisions keeping him as a starter at this stage, but eventually could work into a bullpen role.
Jensen went 5-8 with a 4.55 ERA in 152 1-3 innings for Class A Modesto. He had 136 strikeouts to 39 walks in 28 starts.
In less than 24 hours last week, Beane completed three trades while also working to deal Anderson. The A's acquired new closer Jim Johnson from the Orioles to replace All-Star closer Grant Balfour. Then last Tuesday, they traded for San Diego right-handed reliever Luke Gregerson for Seth Smith and acquired outfielder Craig Gentry from Texas for top prospect Michael Choice.
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