The Hammers on Friday signed off the £105 million deal to sell captain Rice after receiving the paperwork from leading suitors Arsenal.
Confirmation of a move to the Gunners is not mentioned in West Ham's statement but the East London club are now ready to sanction the sale of the 24-year-old midfielder.
Rice posted a farewell message on Instagram, saying: "I can't believe an incredible 10 years has come to an end. West Ham has been a massive part of my life on and off the pitch. Saying goodbye is never easy.
"I've had some unbelievable highs, none higher than that night in Prague. I've also grown a lot as a person, a player and as a captain.
"My connection with the fans means everything to me and my family. You have treated us like one of your own since the day I arrived. Thank you."
In a club statement, joint-chairman David Sullivan said: "I am sorry to see Declan leave us, but I believe that everyone at West Ham United should be very proud of the part we have played in his journey from the Academy of Football at Chadwell Heath to becoming the most valuable young player in English football.
"I would like to make it clear to our supporters that we did not want to sell Declan. We wanted to build our team around him and made a series of improved, long-term contract offers to secure his future.
"However, once Declan made it clear that he wished to move on and seek a new challenge, the Club felt it would not be right to stand in his way, acting in the best interests of West Ham United.
"He leaves with the sincere thanks, respect and love of everyone here, having earned his place in history alongside the great Bobby Moore and Billy Bonds as the only players to have captained West Ham United to a major trophy. More than that, he has always given absolutely everything for the football club throughout his time with us.
"Declan will forever hold a special place in the hearts of Hammers fans and everyone here at the Club. We wish him well for the future and he will always be an inspiration and an example to any young player coming through our Academy."
Meanwhile, manager David Moyes added: "I'd like to personally thank Declan for everything he has done during his time at West Ham United. Obviously it is sad when we say goodbye to someone who has been with us for so long but we must now look forward.
"West Ham United is a huge Club and, as history shows, no player is ever bigger than the Club. Our entire focus now is on building upon the success we enjoyed last season, adding to our talented UEFA Europa Conference League title-winning squad as we enter our third consecutive season in Europe, and continuing to develop the best young talent through our successful Academy."
Rice's pending switch across London to last season's Premier League runners-up Arsenal will bring an end to a lengthy transfer battle.
Mikel Arteta's side saw two bids rejected by West Ham earlier in the transfer window before a breakthrough was made over one week ago.
Arsenal also fended off interest in Rice from title rivals Manchester City, who withdrew from the pursuit after seeing a £90m offer turned away immediately.
Rice joined West Ham as a 14-year-old after being released by Chelsea and progressed through the club's academy before reaching the first team.
He made 245 appearances in total and captained the side which won the Europa Conference League last month, ending the club's 43-year wait for a major trophy.
