Ted Segal, the club’s new majority owner, announced the three-year deal at a press conference on Tuesday.
The 25-year-old leaves Turkish side Yeni Malatyaspor after spending two years with the Super League team.
His contract in Turkey was supposed to run until June next year but the clubs agreed on the transfer, which will see Hadebe arriving at Dynamo Houston as their third most expensive player in history.
However, Hadebe will move to the MLS from Yeni Malatyaspor in July after sorting out his work visas.
He had joined Yeni Malatyaspor in July 2019 from South African giants Kaizer Chiefs.
During his stint in Turkey, he became a key member of the team, in the last two seasons, and has helped Malatyaspor maintain their Super League status.
Hadebe made 53 league appearances, in two years for the club, and has also played a number of domestic Cup games and in the UEFA Europa League qualifying rounds.
In total, he featured in 60 games and had two goals and two assists, despite playing as a central defender.
Other Zimbabweans to play in the MLS are Edward Munjoma, (22-year-old defender), retired Vitalis Takawira, Joseph Ngwenya, Mkhokheli Dube and Mubariki Chisoni.
Hadebe will be battling against Malawi national Victor Wanyama who plies his trade for CF Montreal.
More: Pindula News; The Herald