McCarthy joins for a fee in the region of £12million, while Lukaku makes the move to Goodison Park on loan.
Everton had been linked with Republic of Ireland international McCarthy for some time but the transfer appeared to be off after Latics chairman Dave Whelan baulked at the idea of the fee being paid in instalments.
A deal has now been thrashed out though and the 22-year-old will be back playing in the Premier League having been relegated with Athletic last season.
Meanwhile, Everton boss Roberto Martinez has boosted his attacking options after beating West Brom to the loan signing of Belgium international Lukaku.
Chelsea had initially indicated they would not be letting him leave Stamford Bridge after he impressed on loan at The Hawthorns last season.
Lukaku has played in three of Chelsea's four matches this season but Jose Mourinho has allowed him to make the temporary move to Merseyside, despite West Brom appearing keen to take him back to the West Midlands.