Speaking after Wednesday's Europa Conference League triumph over Fiorentina, Sullivan told BBC Radio 5 Live: "We gave the promise last summer that if he gave us his all, we would let him leave the club.

"It's a fair and proper thing to do."

On Wednesday, Rice became only the third West Ham captain to lift a trophy for the club, following in the footsteps of the great Bobby Moore, who lifted the European Cup Winners' Cup in 1965, and club legend Billy Bonds, who led the Hammers to the FA Cup in 1975 and 1980.

Rice has played 245 games and scored 15 goals for West Ham, having made his debut in the 2016-17 season after coming through the academy.

He represented the Republic of Ireland three times before switching his international allegiance to England, for whom he has been capped 41 times, playing in all five matches at the World Cup last year.

Rice has one year left on his contract, although West Ham have the option to extend that until the summer of 2025, leaving them in a strong position to negotiate a substantial transfer fee.

"West Ham is a very proper club, and we do things in a proper way," Sullivan added. "At the same time, we don't want some club having us over and a replacement is going to cost 50 to 60 million and they're not going to be as good as him."

Sullivan said he was "elated" by the result in Prague and claims he never lost faith in manager David Moyes despite a difficult campaign that saw the club finish 14th in the Premier League.

"It was a lovely night because we've had a terrible season, there's no point saying other than we've had a disappointing season," he said.

"I didn't anticipate it, yet deep down we all thought we'd win this trophy from day one.

"We've been absolutely behind the manager. At difficult times we've rung him up and said 'whatever you read in the papers, you are our manager and you will be our manager at the end of the season'."

Rice was voted Uefa Conference League Player of the Year, while being named in the Team of the Year alongside Alphonse Areola, Nayif Aguerd, Jarrod Bowen, Lucas Paqueta and Michail Antonio.

Former West Ham defender Julian Dicks, part of the coaching staff during Rice's breakthrough season, said his departure would leave a void in midfield.

"He very rarely gives the ball away. That's great for a midfield player. He's an asset to any club and West Ham will miss him," Dicks told BBC Radio 5 Live.

"Players want to win trophies. It can't be about money, as they earn enough. I can't blame Dec for wanting to go and win trophies. If West Ham were winning trophies every other season, I'm sure he would stay."

West Ham legend Trevor Brooking told BBC Radio 5 Live: "Rice has been a leader and driven people on.

"[The] general feeling is he will move on, but what a way. He could have left earlier but, with the way it has ended, he couldn't have asked for any more.

"When somebody leaves a club like that you usually think fans wont be happy, but he is such a credit to the club. We will wish him all the best."