Rodgers was confirmed as new Liverpool boss after the club agreed on a compensation fee of around £5million with the manager’s former employers Swansea.
Henry told the club’s official website: “Fenway Sports Group is committed to building for the long-term.
“Brendan Rodgers’ appointment today as manager of Liverpool Football Club is one of the most important steps we will take in building the kind of club on and off the pitch supporters can be excited about.
“Brendan’s comprehensive football philosophy is perfectly aligned with those at the club and those soon to join the club.
“He was the first choice unanimously among them and he had no hesitation at all in embracing exactly what we want to try to build at Liverpool.
“We do not expect miracles overnight nor should anyone else. But we firmly believe that the direction the club is heading in will lead to Premier League championships.
“We will embrace the unconventional, build the right way and together set a bold, exciting course for this historic club.”