He will sign a two-and-a-half-year contract.
A Scottish representative held promising discussions with his previous team on Friday, ultimately resulting in Moyes being offered a deal until 2027. This will initially require him to prevent relegation, with subsequent efforts focused on the team's development at the new Bramley-Moore Dock stadium.
And the 61-year-old will make his Toffees return, almost 12 years after leaving Goodison Park for Manchester United.
Dyche was removed from his position a few days after requesting payment for the remainder of his contract from the owners, as he felt that his period at the club had come to an end.
History with Everton, a record in relegation battles, and overall availability.
Under-18s manager Leighton Baines and club captain Seamus Coleman took temporary charge for the FA Cup win against Peterborough on Thursday, but Everton felt it was essential to appoint a permanent successor to Dyche.
Moyes becomes the first managerial appointment made by TFG, who completed their takeover in December and put Moyes in charge of the team after he left Everton in 2013.
He takes over a tough challenge at Everton, who have not scored in eight of their last ten league matches and have secured only three top-flight victories all season, sitting 16th in the table, narrowly above the relegation zone, a single point clear.
Moyes' first game back in the hotseat will be against Aston Villa at Goodison Park on Wednesday. He was originally hired in 2002 and had 518 games under his belt during his first stint on Merseyside.
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