The Aston Villa player will spend the season with the Scottish champions. The deal includes an option to buy the 24-year-old next summer.
Midfielder Petrov spent seven years with Celtic before taking the opposite path to Tonev, by moving south of the Border to join Villa.
The winger said: “Joining Celtic is unbelievable, and I feel really good about it.
“I already knew all about Celtic. Everybody in Bulgaria knows Celtic.
“I spoke to Stiliyan Petrov yesterday and he was very happy for me. He wished me good luck and I hope I can do as well for Celtic as Stiliyan did.”
Tonev has been joined at Parkhead by Manchester City defender Jason Denayer. The Belgian has signed a season-long loan deal.
Tonev has won 15 caps for Bulgaria and Villa hoped he could be a Premier League threat when Paul Lambert signed him from Lech Poznan in June 2013, but he only made eight starts last season.
Celtic manager Ronny Deila believes Tonev has more to offer than he showed in England.
Deila said: “Aleksandar’s a very quick player and he has two good feet which he can shoot with. He has scored a lot of goals during his time at Lech Poznan and I think he can help bring the club forward with his qualities. We can also make him better.”