Harry Redknapp, the Saints manager, knew nothing of the 24-year-old's move until the deal had been done, with Liverpool paying £3m upfront.
"I just got a message a while ago that they [the Southampton board] had agreed terms with Liverpool, so that is where he is now," Redknapp said.
"A fee of £7m is good money and, obviously, it was too good to turn down," he added. "I would love to have kept him. He was a key player. I am sure he will be a big success there."
Crouch, who made his England debut in a 3-2 friendly win over Colombia in May, hit 12 league goals for Southampton last season, but they were not enough to save the club from relegation from the Premiership.
He will become the European champions' sixth summer signing and will take their spending past the £20m mark.
Rafael Benitez, the Liverpool manager, has been chasing the player throughout the summer and it appears the club's third bid proved acceptable.
Crouch caught Benitez's eye with a good display in Southampton's 2-0 win over Liverpool at St Mary's in January, where he scored Southampton's second goal.
Meanwhile, Liverpool are bracing themselves for a storm of criticism from Australia over their medical treatment of Harry Kewell as the Anfield winger undergoes his second operation of the summer.
Kewell last kicked a ball for Liverpool in the Champions' League final in Istanbul and had to be replaced by Vladimir Smicer before the break.
Kewell had an operation soon after the final to repair an adductor muscle tear, amid claims that he lacked commitment.
Now, with the season just a few weeks away and Liverpool involved in a crucial qualifying campaign for next term's Champions' League, Kewell entered hospital again yesterday for a hernia operation.
It is just another in the seemingly constant injury problems suffered by Kewell last season, when Liverpool fans lost patience with the former Leeds player, while Benitez also showed his displeasure at the winger's attitude.
Kewell had support from his agent Bernie Mandic and the former Australia coach Frank Farina, who openly criticised the medical treatment their man was receiving at Anfield.
Liverpool's statement on their website yesterday pointedly explained that the new surgery was nothing to do with the operation he had after the European final. It said: "The injury is unrelated to the adductor tear operation the player underwent following the Champions' League final."
But there is likely to be some criticism from Australia that this is a further problem for the player in an area of the body close to the last injury.
Kewell constantly complained that he had serious injury problems in the groin area and openly questioned whether he should have an operation before the season ended.
Liverpool now say that Kewell will be back playing again in five to six weeks, but yesterday's operation could mean that the player's fears were justified.
Sami Hyypia has responded to claims that Benitez is about to bring in a new central defender, Real Zaragoza's Gabriel Milito, in a £10m deal. "On the first day back in training the gaffer told me a new centre-half would be coming," Hyypia said. "I just said, 'Bring it on'. Whoever joins this club has to earn his place in the team as much as everyone else."Reuse content