The 26-year-old was eager for a move away from Upton Park, after failing to secure a regular first-team berth in the Premier League, and handed in a transfer request.
There was reported interest from a number of clubs, including Swansea City and Norwich, but manager Sam Allardyce was not keen on letting the striker, who made 24 league appearances last season, leave.
And with the window shutting on Monday, Nolan has insisted that the players will do everything they can to make him feel wanted at the club and help him flourish.
"Obviously we had the Ricardo Vaz Te incident last week but hopefully now he can just knuckle down and fight for his place and really it's about us making sure he knows he is still wanted here," he told the club's official website.
"At the end of the day, we're a tight-knit group and we were surprised by it but that's football and that's life.
"Hopefully now we can put it all to bed and he can get back amongst the lads because we're all waiting with open arms.
"Generally he just wants to play football and hopefully now he'll get the chance. It's up to him to prove everyone wrong."
Vaz Te will also potentially get the chance to link up with former partner Carlton Cole in the coming weeks, with the 29-year-old poised for a return to West Ham after being released in May.
The decision to look to bring Cole back came after the club failed to bring in any more forwards during the window, apart from clinching Andy Carroll permanently following a successful loan spell.
