The 56-year-old Scotsman, whose reputation took a battering during a deeply unsuccessful spell as Manchester United boss in 2013-14, signed an 18 month contract with the Premier League strugglers on Sunday.
Moyes was let go by co-owners David Gold and David Sullivan after the 2017-18 season despite leading the club to survival and a 13th-place finish.
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He was replaced by Manuel Pellegrini, whose tenure came to an end on Saturday following the 2-1 home defeat by high-flying Leicester City which left the Hammers fourth from bottom just a point above Aston Villa.
Moyes, who established his reputation with Everton before the demoralising spell at United, said he was not bitter about being let go in 2018.
"No, because things were done correctly -- I wasn't taken on and I was told that," he said on Monday at a press conference ahead of Wednesday's home game with fellow strugglers Bournemouth.
"I was disappointed, I've said that, but I've got another chance to go again.
"I think it says a lot about the owners, they thought the job I did was good enough to give me another opportunity.
"This time I'm going to make it so there's no choice but to renew.
"There's a clause in there and I'm going to make it impossible to ignore that, that's my plan."
Moyes, who also had unsuccessful spells at Spanish side Real Sociedad and Sunderland, said he had not hesitated when he received a phone call from the owners.
"It was very simple when they called me," he said.
"They asked me do I want to come back and I said 'I can't wait'.
"We didn't talk about the past, we were just talking about the team now, what we have to do and the position we're in."
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Moyes return has not been universally welcomed by West Ham fans but he said he was the right fit for the job.
"What anybody's getting is a very experienced Premier League manager, I think there's arguably only two or three more experienced around, and I win," he said.
"There's a lot of new modern things in football but recently I think you've seen signs of things going back a bit.
"We do want to keep possession but perhaps possession is not now seen, even maybe by yourselves (in the media), as the key to winning games.
"The fans want to see more attacking football, action and excitement.
"The biggest thing I want to see from my team is for the supporters to be excited -- I would love that to be the case."
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