After the forward scored seven times while on loan last term, despite reoccurring injuries, the ex-Hammer thinks the 24-year-old will benefit from a regular and important role
The striker completed a club-record £15.5 million transfer to the east Londoners on Wednesday, signing a six-year deal after notching seven goals while on loan from Liverpool last season.
And Cottee - who netted just under 150 goals over two spells with the Hammers - reckons the 24-year-old will be a long-term success for Sam Allardyce, labelling his capture a "massive statement of intent".
"I'm absolutely delighted," he told the club's official website. "We've all been waiting patiently since the end of the season but I think it was clear from the start that Andy wanted to sign for the club.
"We saw some real quality glimpses from Andy last season and we can now look forward to him starting the season as a permanent West Ham player. It's a big signing for the club.
"It's a massive statement of intent from the board and they need congratulating for bringing a player of Andy's standing to the club.
"I'm pleased it's a long-term contract and hopefully he can be the man who can lead us to stability, and hopefully Andy will be leading the attack for the next six, seven, eight years for the club."
The 47-year-old suggested the ex-Liverpool forward is a good fit for the West Ham team and hinted the move could see him rediscover his top form and force his way into Roy Hodgson's World Cup plans.
He continued: "For the way Big Sam wants to set his teams up, I think Andy slots right in for him. Playing in the system with Kevin Nolan pushing on from midfield, they have a telepathic understanding and they got on really well on and off the field.
"With Kevin pushing forward you need a big target man, you need someone who is going to hold the ball up, bring the others into play and then if you get the likes of Matt Jarvis supplying the crosses, he's always going to be a danger.
"Whatever club you go to, it's great to get that adulation from the fans, when they respect you as a player and understand what you bring to the table.
"Andy will get that, and I think from his point of view there's a World Cup at the end of next season, and if you're not playing football you won't be in Roy Hodgson's plans."