The ex-Scotland international joins the Toffees a month after his sacking as Fleetwood Town manager following a run of one win in 11 matches.
Adam, who has been appointed as the club's new set-piece coach, joins former Everton winger Alan Irvine in Moyes' backroom team.
The Everton boss said: "I'm delighted to have been able to add Alan and Charlie to our coaching staff.
"Obviously, Alan is somebody who I have known for a very long time and have tremendous respect for. His knowledge of the game, as well as his understanding of what is required at Everton - a club that means a lot to both of us - will be invaluable.
"Charlie is someone I have had several chats with since rejoining the Club. He will be helping with set-piece situations, an area he excelled in as a player and one I believe he can really help us with now as a coach.
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"The two of them, along with Billy McKinlay and Leighton Baines, give us a really strong coaching foundation as we look to make positive strides forward."
Adam rose to prominence during a spell at Blackpool which was helped by Sir Alex Ferguson's ringing endorsement of his set-piece ability.
After a match between Manchester United and Blackpool in 2011, Ferguson said: "We just couldn't handle Charlie Adam's free-kicks and corners.
"We were all over the place. His corner kicks are worth £10million in themselves.
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"The boy is an incredible striker of the ball."
Moyes will be hoping he can tap into Adam's unique skillset as he bids to steer the Toffees clear of danger in the second half of the season.
His addition is likely to add extra spice to what is set to be a mouthwatering Merseyside derby at Goodison Park on February 12.
The fixture was postponed earlier in the season due to adverse weather conditions and fans will be hoping Adam's know-how can inspire a repeat of last season's 2-0 win over the Reds.
Adam will return to Anfield in the reverse fixture on April 2 in what is likely to be an emotional moment for the Scot.
Liverpool paid Blackpool £6.75million for Adam in 2011 but his stay was short-lived.
The midfielder played 37 times for the Reds, scoring twice and registering six assists before completing a move to Stoke City the following summer.
Speaking to Sky Sports about his Anfield exit, Adam previously revealed that he regretted leaving the club at the time and wishes he'd have stayed to prove his worth to then boss Brendan Rodgers.
"It was a difficult choice but one of those decisions you have to make," Adam said.
"I only had 24 hours to think about it. We played Hearts in the Europa League on the Thursday night and I went to see Brendan and said 'what's the situation?'
"He said, 'we want to sell you' and that was it. In 24 hours I made the decision (to leave) but I probably should have stuck it out for another season if I'm being honest.
Adam joins a distinct group of players to have represented both Merseyside clubs.
Nick Barmby turned out for both the red and blue half of Merseyside as did Don Hutchison, Conor Coady, Sander Westerveld.
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Going back further, Peter Beardsley and Steve McMahon represented both clubs as did Kevin Sheedy, Gary Ablett and Abel Xavier.
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Meanwhile, former Toffee Johnny Heitinga is currently part of Arne Slot's coaching team at Liverpool.