Goalkeeper Hart joins from Tottenham on a three-year deal while McCarthy has penned a four-year contract following his summer exit from Crystal Palace
The Hoops will be hoping both men can have a positive impact on the squad after a difficult start to the season.
Manager Ange Postecoglou said on the club’s official site: “I’m delighted that we have signed two top-class players in Joe and James.
“Both of them have a wealth of experience at both club and international level and that is something which can only benefit the squad, and I’m looking forward to working with both of them.
“I know our supporters will be well aware of both players, and I’m sure they’ll welcome them to the club and look forward to seeing both of them play for Celtic in the seasons ahead.”
Hart, the 34-year-old former England and Manchester City goalkeeper, played 10 times for Spurs last season but only in FA Cup and Europa League games. He has left Spurs for £1million with a year to go on his deal.
Postecoglou started the season with Greece international Vasilis Barkas, signed last year from AEK for a reported £5million fee, between the sticks but he has been replaced by Scott Bain in what is widely perceived as a problem position for the Parkhead club.
Hart said: “This is a great moment for me in my career and I am absolutely delighted to be joining a club of Celtic’s stature.
“I know just how big this club is and of the incredible support that it enjoys, and I can’t wait to play in front of the fans at Celtic Park.
“I’m looking forward to meeting up with my new team-mates now and getting to work with the squad and, in particular, the other goalkeepers here.”
McCarthy returns to Scotland 10 years after leaving Hamilton following distinguished spells at Wigan, Everton and Palace.
The 30-year-old, who is a Republic of Ireland international, joins after two years at Selhurst Park.
He added: “To have signed for Celtic is a brilliant feeling and this is a special day for me and my family.
“I know all about the club, the size of it and all the success it’s enjoyed, particularly in recent years. I’m looking forward to pulling on the Hoops, playing at Paradise and helping the team deliver more success to these amazing fans in the seasons ahead.”
Postecoglou’s side are preparing to face Czech hosts Jablonec in the first leg of their Europa League third qualifying round on Thursday.
Celtic have already been knocked out of the Champions League qualifiers by Danish side Midtjylland and lost 2-1 to Hearts at Tynecastle in their cinch Premiership opener at Tynecastle on Saturday night.