The deal also includes a full no-trade clause, according to the source.
Houston missed the playoffs this year after winning the AL wild card in 2015.
The switch-hitting Beltran, who turns 40 in April, was the top player in the deadline-selling Yankees' lackluster offense this past season before being traded to the Texas Rangers on Aug. 1 for right-hander Dillon Tate and two other pitching prospects.
He led the Yankees with a .304 batting average, 22 homers and 64 RBIs, and he finished the year with 29 homers, 93 RBIs and 163 hits. He split his time as a designated hitter and right fielder.
The nine-time All-Star signed a $45 million, three-year contract before the 2014 season but played with an elbow bone spur during much of his first season in New York and got off to a slow start in 2015 following surgery.
Beltran was traded from Kansas City to Houston in June 2004, and he hit a record-tying eight homers in 12 games during the NL playoffs while batting .435 with 14 RBIs.
He also was traded from the New York Mets to San Francisco in July 2011. While he has appeared in the playoffs with the Astros, Mets, Cardinals, Yankees and Rangers, Beltran remains in search of his first World Series title.
Beltran has a .281 career average with 414 home runs.
Led by middle infielders Jose Altuve and Carlos Correa and ace Dallas Keuchel, the Astros ended a decade-long playoff drought -- and reversed a four-year span in which they averaged well over 100 losses -- by winning the AL wild card in 2015. Expected to be a championship contender this year, Houston instead went 84-78 and missed the playoffs.
The Astros have been busy since then, signing Reddick to a $52 million, four-year deal after he finished the season with the Dodgers and getting McCann, a seven-time All-Star, in a trade with the Yankees. The Astros got $11 million from the Yankees to help cover the $34 million total he's set to make in the next two seasons.
Along with his production on the field, Beltran has long been praised for his clubhouse influence and leadership, especially among young teammates. Beltran also runs an academy back home in Puerto Rico, where students focus on academics as well as athletics.
The Associated Press contributed to this report.