The England stopper became Koeman’s fifth Saints signing on Saturday, joining from Celtic on a four-year deal.
And the coach gave his latest acquisition a resounding review, saying that the 26 year-old has the perfect blend of experience and potential.
“He’s England’s third goalkeeper, he has a lot of experience and he’s played at Champions League level.
“The squad is young but, like the other goalkeepers in Kelvin and Artur, he is experienced and we need that type of person in our squad.
“But goalkeepers normally have a longer career than outfield players, so this is about the future,” he continued.
“For the next three, four, five years, we have a very good goalkeeper.”
Koeman says Forster will go straight into his team, with the decision to bring in the Northumberland man influenced by the fact Artur Boruc is out of contract next year.
“Everybody knows the situation with Artur Boruc – it’s the last season of his contract – so this is a choice about the future,” he explained.
“I’ve already spoken to Artur, and Fraser Forster comes in as the first goalkeeper. Artur has to give real competition, and I expect that because that’s the professional way.
“It’s a difficult situation for him, I understand that, but it’s football. We need competition in all of the positions.”
Koeman says Forster’s capture demonstrates Southampton’s current aspirations, adding that his business may not be over as the side’s Barclays Premier League opener against Liverpool moves closer.
“We’ve showed that the club and everybody in it still has really good ambition,” said the Dutchman. “We know that we’ve lost five good football players, but now we’ve brought five in.
“We need one or two more in other positions, but we’re showing our ambition – I like that.
“We need time because it’s a pre-season of rebuilding the team, but in football you don’t have time. Next Sunday we play against Liverpool away and that brings points, so we have to be prepared for that.
“I was at Anfield yesterday to watch Liverpool against Dortmund,” he continued, having spent Sunday watching the Reds beat their German opponents 4-0.
“It’s a great stadium with a lot of history, and we’re looking forward to playing against them.
“They played well, but we have to understand that Dortmund was very poor. They didn’t make it difficult for Liverpool, but we will do that.”