Moyes has signed an 18-month deal and starts with the New Year's Day home game against Bournemouth at London Stadium.
He replaces Manuel Pellegrini, who was sacked after Saturday's 1-2 home defeat by a much-changed Leicester side.
"It's fabulous to be back," Moyes said in an official statement.
"It feels great to be home. I've missed being here because I really enjoyed it. I enjoyed being around the stadium and I loved being in this part of the world and I missed the club, so I can't wait to get started.
"I'm feeling very proud that I'm back here at West Ham. But I think more importantly I'll be looking to see what I can do and what I can make improvements to, how we can get some wins with the players and how we can get some quick wins on the field as well.
"I do believe that the squad of players I've got here is a better squad of players than when I took over before, so I am looking forward to working with them.
"I think there's got to be a short-term goal for us just now to get the wins to get us away from the wrong end of the league and what we're going to do over the next six months, then what we're going to do over the next period as well. The start is really focusing on the immediate games."
Moyes has managed in the Premier League for 15 seasons, including a successful spell at Everton which earned him a move to Manchester United.
Joint-Chairman David Sullivan said: "David proved in his short time with the Club that he was capable of getting results and we believe that he will start moving the club in the right direction once again.
"We are delighted to welcome David back - he knows the club well and he built strong relationships during that time which will be crucial for the work that needs to be done going forward."
( With inputs from IANS )