Baxter joined Everton at the age of six and progressed through the youth ranks before becoming the youngest player to debut for the club at the start of the 2008-09 season at the age of 16 years and 191 days. The 21-year-old joined Tranmere on loan in September 2011 and turned down a new deal with the Toffees when it was offered later that season.
Instead, Baxter signed up for npower League One side Oldham where he has been an ever-present this season, scoring 11 goals, and now he takes on his old club in Saturday evening's fifth-round clash at Boundary Park. And Moyes said: "I'm delighted for Jose. It (leaving) was a brave decision for Jose, and hopefully he sees it as being the right one for him."
He added: "We gave him his debut when he was 16 years old, and it's hard when you come in that early because by the time you get to 19, 20, people are beginning to ask 'Where are you? What are you doing?'
"He probably found it a struggle getting into the first team very early, so we put him out on loan. We then offered him a contract and he could have stayed, but the boy wanted to play, so he chose to go.
"I admire that because there are a lot of players who don't choose to do that, who would prefer to sit and hang around."
Asked as to Baxter's prospects of returning to the Premier League, Moyes said: "He certainly has the ability, he has a very good football brain, and because of that he's a gifted and talented player.
"I watched him play for Oldham last week and he did very well. Jose will have a long career, I've no doubt about that."
Moyes should have Sylvain Distin available after the defender missed Sunday's 2-0 defeat at Manchester United through illness.
Striker Victor Anichebe is a doubt, however, with a knock sustained in that game which saw him substituted just before the hour mark.