Roman, 46, the assistant head coach and tight ends coach last season, coordinated the Ravens' dominant running game while Mornhinweg called the plays. Much of the system that Baltimore ran with Jackson mirrored what Roman had done with Colin Kaepernick when Roman was the offensive coordinator in San Francisco, from the pistol formation to the read-option plays.
Mornhinweg, who had been the Ravens' offensive coordinator since October 2016, will not return to Baltimore.
"We tried to keep Marty, but he has decided to move on, and I respect that," said Ravens head coach John Harbaugh. "He's a really good coach and helped us win the AFC North last season and get close to the playoffs the previous two years."
This reshuffling allows the Ravens to keep Roman from becoming a coordinator elsewhere, ends speculation that Harbaugh will coach elsewhere in 2019 and puts Jackson on his best path for success. In his rookie season, Jackson went 6-1 as a starter and led all quarterbacks with 695 yards rushing.
"Increasing Greg's responsibilities will help us get where we're going on offense," Harbaugh said. "His role with our offense has already been significant and substantial. His understanding of the run game we are building -- which we saw some of in the second half of the season -- and how it integrates with a consistent and big-play passing game is exciting."
Mornhinweg's demotion comes five days after the Ravens produced a season-worst 229 total yards in a 23-17 loss to the Los Angeles Chargers in a wild-card playoff game. Many Chargers players said after the game that they could anticipate what the Ravens were running because they hadn't changed their game plan from the previous meeting a couple of weeks earlier.
In his second season with the Ravens, Roman turned a struggling running game into one of the league's best. Baltimore, which ranked 28th in rushing in 2016, finished No. 11 in 2017 and No. 2 last season. With Jackson, the Ravens rushed for at least 190 yards per game in the final seven games of the regular season, becoming the first team to do so since the 1976 Pittsburgh Steelers.
Left tackle Ronnie Stanley referred to Roman as "a genius" earlier this week.
"He calls a lot of great schemes against a lot of these tough defenses in the NFL," Stanley said.
This is Roman's third NFL offensive coordinator job. He had that role under Jim Harbaugh in San Francisco (2011-14) before calling the plays in Buffalo (2015-16). Roman's offenses have centered around mobile quarterbacks, from Kaepernick to Tyrod Taylor.
Roman becomes the sixth offensive coordinator under Harbaugh, following Cam Cameron, Jim Caldwell, Gary Kubiak, Marc Trestman and Mornhinweg.