Kouyate, who joined West Ham for an undisclosed fee from Anderlecht on a four-year deal, becomes the club’s second summer signing following the arrival of Argentine striker Mauro Zarate.
Allardyce told the club's website: "We're delighted to have secured what has been one of our top targets so early in the pre-season. Kouyate is a dynamic midfielder, goes box to box and has excellent skills with both feet as well as being strong in the air.
"If needed, he can fill in at centre back but his strength will be what he can do in midfield and creating the chances we need to attack.
"He is only 24, so a good age and he was insistent that West Ham was his choice of club. Valencia and a few other top clubs were after him, but he wanted to come here and I am looking forward to him having a bright future here at West Ham.
"The importance of getting a top target so early is vital to that player being here for the start of pre-season, especially coming from abroad. He can get to know his team-mates at the beginning and integrate himself and bond with the rest of the team before the season begins, we get to know what he is about and he gets to know about us.
"It has been a long pursuit, with the joint chairmen, myself and Martyn Glover to get him, but we have got him and we look forward to seeing him in a West Ham shirt in the new season."
West Ham will kick off the new season with a home game against Tottenham and Allardyce is looking forward to facing Mauricio Pochettino's side.
He added: "What a game to start the new Barclays Premier League campaign with - I am sure our fans are rubbing their hands with delight as it is the fixture they look out for every season.
"And after beating them three times last season, the pressure is on to do it again and in the first game of the season as well, so we will have to be ready and keep the results going against them!
"It is a tough start, there is a real mix of teams we are playing in the first seven games, in terms of sides who you look at being at the top, the middle and two newly promoted sides in Burnley and Queens Park Rangers.
"It is quite unusual to have so many local derbies in the first set of games, after Tottenham, we go to Crystal Palace and then QPR, so it's tough but as we know, every game is tough in the Premier League."