Bregman's new deal will reportedly buy out his three arbitration-eligible years through 2022, and his first two years of free agency through 2024.
The reported agreement will also be tied for the second-highest contract in club history, trailing only Jose Altuve's five-year, $151-million deal signed last March.
Bregman recently voiced his disappointment with the renewal process for pre-arbitration players when he was only given a $41,500 raise earlier in March after a terrific 2018 season.
The 24-year-old is coming off a campaign that saw him slash .286/.394/.532 with 31 home runs and 103 RBIs. He made the All-Star team for the first time and finished fifth in AL MVP voting.
Houston finished first in the AL West last season with a 103-59 record before the Boston Red Sox knocked them out of the playoffs in the ALCS.