Gerrard's contract will expire in June and the 34-year-old will seek a new challenge away from England, with a move to the MLS widely reported.
Since taking over at Anfield in 2012, Rodgers has been impressed with Gerrard's impact and paid tribute following the captain's announcement.
"It is almost an impossible task to find the words to appropriately sum up Steven Gerrard and his importance to Liverpool," he told the club's official website.
"This is an era where the word 'legend' is vastly overused, but in his case it actually doesn't do him justice.
"From a personal point of view I will always have gratitude for the support he gave me, when I arrived here as manager.
"Steven came to see me and promised he would be 100 per cent behind me and do everything he could to help as we looked to introduce new ideas and a new way of working.
"He wasn't just true to his word, he vastly exceeded it.
"As a player he is immense and the influence he has on games should never be understated. At times he has carried this club on his back and in my time here he has always shown the ability that has rightly seen him be regarded as one of the world's best for well over a decade.
"As a leader and as a man, he is probably incomparable to anyone I have ever worked with.
"He takes professionalism to a new level and the dedication he has to his work is an example to everyone in the game.
"He is also someone who has always put the club and team ahead of himself and I think that will ultimately be his legacy.
"People better placed than me to judge have said Steven is Liverpool's greatest ever player; when you look at the company he is in, that is some statement.
"We of course will miss him, both on the field of play and in his capacity as club captain, but his influence will live on and we wish him nothing but joy and success wherever he chooses to go next.
"Until that moment arrives I will continue to enjoy working with Steven Gerrard the man and Steven Gerrard the player, one of the greatest we have seen."
Liverpool owners John W Henry and Tom Werner echoed Rodgers' comments about the club's captain, and admitted they hoped he would return in another capacity in the future.
In a joint-statement they said: "His contribution to the club is almost beyond measure and it's testimony to his influence, that despite Liverpool having such a long and distinguished list of legendary figures, the name Steven Gerrard will always be at the summit.
"Steven will always have a part to play for this club, as and when the time comes that he wishes to return.
"We all wish him well in this endeavour and look forward to welcoming him back to Anfield in the future, when the time is appropriate."
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