Bobby, along with Jobi McAnuff, also in the travelling party to Bradford, hopes to make his Hammers debut at Bradford and Peter insists he has the quality to make the grade at Upton Park after a relatively brief Tottenham career.
He reckons that Bobby not making the impact he would have wanted at White Hart Lane - had a simple explanation - he wasn't given the chance.
"I don't think that was really down to Bobby; if you had seen Spurs playing it has been a club with a bit of turmoil and never really a settled side," he explains.
"As a striker you are dependent on service and I don't think he has been getting that; I think if he had he would have scored goals.
"And as a young man going into the Premiership you need games to get up to speed, there is no doubt about that.
"Hopefully their loss will be our gain; you can see in his eyes he has the desire to do well and he has got an affinity with the club which, to be fair, you can't really buy in the modern day game.
"He is really excited about coming here and we are really excited about working with him because he really is a wonderful talent.
"I think he will prove a fantastic signing and he has a lot to prove to people; not us - because we know what he can do - but outside people.
"He has played in the division before and I am sure he will end up another hero.
"We still have a lot of good players up front with David Connolly, Marlon Harewood, and Brian Deane who have all been scoring goals and hopefully if you add Bobby to that we will have the cutting edge that you need at the top level.
"Bobby is a different type of player to Jermain and gives us different options; we still think there is more to come from him and we hope he can show that for West Ham United.
"He has the chance to fulfil the dream of scoring in front of his own supporters - hopefully that dream will come true and we will head back to the Premiership."
As for the departure of Jermain Defoe, Peter is philosophical.
"As I have said many times before I think he could play for Real Madrid because if you give him a chance he will score goals," says Peter, "but I think we have got to look at the positive aspect and say it is good we have got a player of the quality of Bobby Zamora who I have seen a hell of a lot of and coached a team to try and nullify him in games.
"He is a very, very difficult one to look after and although I am disappointed to lose Jermain I am very excited about working with a talent like Bobby.
"Jermain has been suspended for 12 games and if he had scored in them who knows where we could be sitting in the league?
"We are disappointed as a club to lose him but with the money we are getting and a player of the calibre of Bobby it is a good deal."
He admits to being as surprised as Alan Pardew that the deal went through at the 11th hour and adds:
"There is never a day in football without something happening; we got the first phone call and knocked it on the head, then we got the second and everything happened quickly.
"We have replaced the Di Canios and McAvennies and Cottees in years gone by so all of a sudden you have to replace Jermain Defoe.
"I can understand his decision and if he wants to play in the Premier League I have no problem with that.
"I would say he has been a pleasure to work with, both at Bournemouth and the two weeks I have been here.
"We have to look forward and I think the future is bright; there are exciting times to come, there is no doubt about that."
There could have been even more activity if West Ham had managed to capture a full back from Peter's old team Celtic, Stephen Crainey, who, according to reports, was on his way here when in fact he signed for Southampton on loan.
Ironically, he made his debut in a Saints' shirt at Upton Park midweek in the reserves, and Peter admits there was interest.
"He is a wonderful player and we are just disappointed that is was too late," he says of the 22 year old.
"You had to get the Scottish thing done by Friday with the paper work in place and by the time Martin O' Neill got back to us everything was up and running with Southampton.
"Stephen phoned me and said he wanted to come to us but the way everything was going to happen it was going to be too quick and we never had the time to do that.
"So I wish him well but at the end of the day we have got a squad here that people want to come to, and that is the big, big difference.
"The board are desperate for success and we are all pushing the same way; I think the supporters are starting to buy it now.
"Obviously there is disappointment at losing good players but I think they can see we are trying to build a squad of young players to get people talking about West Ham United again in a positive way."
Peter was pleased with the win over Rotherham in front of a full house and says:
"I said to the boys before the game that I have played under that pressure when there is expectation.
"The players have got to understand they are expected to entertain as well as win and they are desperate to do that.
"We could have been out of sight in the first half when we played some exciting football but perhaps West Ham is a bit like Celtic in that they keep the fans biting their nails right to the death!"
And that seven games a week wish?
"We have a young team with a lot of exuberance and we wish we were playing every day because we want to see this team gel as quickly as possible and hopefully get us to the promised land," he smiles.
SQUAD: Bywater, Shaaban, Mullins, Repka, Melville, Dailly, Harewood, Harley, Carrick, Reo-Coker, Etherington, Connolly, Deane, Quinn, Ferdinand, Zamora, McAnuff, Nowland.