The Ravens also will hire Rick Dennison, Kubiak's offensive coordinator in Houston, as quarterbacks coach, according to sources.
Kubiak, who was fired by the Texans in December, and Dennison both met with Ravens officials Sunday in Baltimore, sources said.
Kubiak will replace former offensive coordinator Jim Caldwell, who was hired as Detroit Lions coach earlier this month.
Baltimore struggled offensively this season, ranking 29th in the league in total offense and 25th in scoring.
The Ravens averaged a franchise-worst 3.1 yards per carry and Joe Flacco threw a career-high 22 interceptions one year removed from winning the Super Bowl.
Kubiak was fired Dec. 6 amid the worst losing streak in Texans franchise history. Houston concluded the season with 14 consecutive losses, including three under interim coach Wade Phillips.
The 52-year-old Kubiak went 61-64 in seven-plus seasons with the Texans, coaching Houston to playoff appearances in 2011 and 2012. He previously served as a longtime offensive coordinator of the Denver Broncos, working under Mike Shanahan from 1995 to 2005.
Kyle Shanahan, who was fired along with his father by the Washington Redskins on Dec. 30, had been a candidate for Baltimore's offensive coordinator.
Coach John Harbaugh named three other candidates -- Ravens receivers coach Jim Hostler, former Lions offensive coordinator Scott Linehan and Pittsburgh Steelers running backs coach Kirby Wilson -- last week.
ESPN.com Ravens reporter Jamison Hensley contributed to this report.