The 22-year-old became Neil Lennon's 10th summer signing after a recommendation from the Celtic manager's former midfield partner, Paul Lambert.
Forster played 39 times for Lambert last season to help Norwich win the League One title, and the 6ft 7in keeper is determined to enjoy a similarly successful spell in Scotland.
Forster's route to the Newcastle number one jersey was blocked by Steve Harper, who has established himself following years in the shadow of Shay Given before the Irishman's move to Manchester City.
Zaluska has not looked entirely convincing in the Celtic goal since Artur Boruc departed for Fiorentina and Lennon was keen to add someone who could push the Pole all the way.
Forster intends to do just that and he believes his title-winning experience at Norwich will prepare him for the demands of playing in goal for Celtic.
"For me it was always about getting out and playing," Forster said.
"Harps had a fantastic year last season and kept a lot of clean sheets.
"Quite rightly he has started the season as number one at Newcastle.
"He has waited a long time for his chance and he has taken it, and no doubt he will hold on to that shirt.
"But I've said all along, even when I was at Norwich, that I wanted to be playing football. I don't like sitting on the bench.
"I'm here to provide competition and I aim to be number one. I'm going to work as hard as I can and hopefully prove to the gaffer I should be playing.
"I've got to prove week in, week out, if I'm playing, that I'm worthy of the shirt."
Forster had short loan spells with Bristol Rovers and Stockport but he really came of age at Carrow Road last term.
"It was a very different experience last year where the pressure is on and everyone wants to beat you," he said.
"Obviously here is a much bigger scale but it's all about winning games and it's fantastic to get the chance to come to a big club where you are expected to win every week.
"Paul Lambert told me what a big club it was and I relish the chance to come and perform.
"He didn't have to sell it to me. He was a fantastic player here and did a lot for me last year, and I can't thank him enough for that.
"He told me I should get myself up here and sign the papers as quickly as possible."
Forster trained with the Celtic squad for the first time this morning after first being made aware of the club's interest last week.
Forster, who has never made a first-team appearance for Newcastle, is ineligible for Thursday's clash against FC Utrecht in Holland and may not be ready for the Clydesdale Bank Premier League clash at Motherwell on Sunday.
"Obviously I can't play in the Europa League on Thursday and I have missed a few games with a slight hip injury but I'm okay now," he said.
"I'm just getting fit, I missed a few weeks and had a few days' training. I've been working hard in the gym and it shouldn't take too long."