The move for McArthur adds further strength to an ever strengthening squad as Martinez looks to finalise the transition of Wigan Athletic Football Club to his style of football.
The midfielder had a choice of clubs this summer and it is a reflection of the exciting Wigan team that Martinez is building that he chose the Latics.
Martinez said: "James is a really exciting prospect," he said, "and we are all delighted that he is chosen to join Wigan Athletic. We are building a squad here at the DW and I see James as being another real quality addition who will add great competition in the midfield areas.
"He is young, hungry, desperate to play for us in the Premier League and I believe he has all the attributes you need to be a success at this level. We want James to feel at home here, enjoy his football and progress his career as he helps with his daily standards, to make Wigan Athletic a stronger football team.
"We have all seen how well James McCarthy adapted to life at Wigan and James McArthur has the potential to be just as impressive.
"James has played a huge amount of games for a player of his age and his desire and winning mentality will be a great asset for our squad."
Speaking to the club's official website Gary Caldwell said of McArthur: "I have played against him a few times for Celtic and he's a real competitor, he's got a never say day attitude and is full of energy and aggression in the middle of the park. He's a fantastic young footballer and I'm sure he'll fit in really well here."
If he proves to be as good as McCarthy then Martinez will have unearthed another bargain buy.