The 56-year-old saved the club from relegation in a six month stint at the helm in 2017-18 and returns with the task of lifting a side languishing in 17th in the standings and a point above the drop zone.
Moyes said he had been given a second chance on the back of what he had achieved last time around, when he had been disappointed not to be retained, and could not wait to get started.
"This time I'm going to make it where there's no choice that they will always want to renew in the future," the Scot told reporters.
"I'm really that thrilled to go again and I'm going to make it impossible that the clause can't be implemented," Moyes said of an 18 month contract that contains an extension clause. "That's my plan and now its for the players to carry it out."
The Hammers turned to Moyes on Sunday after sacking Chilean Manuel Pellegrini, who had been in charge for 18 months.
The club said on Monday that their director of football Mario Husillos and coaching staff members Ruben Cousillas, Enzo Maresca, Jose Cabello and Felix Cao had all left with Pellegrini.
Moyes said former assistant and fellow Scot Alan Irvine would be part of his backroom staff with former West Ham defender Stuart Pearce also in the frame.
"He's certainly one of the people who is under consideration," said Moyes of Pearce, who has other commitments to resolve. "It might just take us a few days to get things sorted."
Moyes' first game will be on Wednesday at home to fellow strugglers Bournemouth, and his appointment has had a lukewarm response from fans on social media.
The former Everton, Manchester United and Sunderland boss responded to the doubters by saying West Ham were getting one of the most experienced Premier League managers available.
"I think there's only two or three managers with a better Premier League win record.
"That's what I do, I win. And I'm coming here to West Ham initially to try and get us wins and away from the wrong end of the table," he declared.
"My bigger picture is to have a strong team, a really good footballing team, attacking team and all those things I have to bring to the table and hope to do so."