The Bulgarian winger will join Craig Gordon and Jo Inge Berget as the Norwegian manager's first recruits, with the club having the option to buy after the year-long loan.
And the Hoops are hoping to add at least one more player before Monday night's 11pm registration deadline for the Champions League play-off round.
Tonev was the subject of a £2million bid by the Hoops last summer.
But, after Celtic agreed a deal with his then club, Lech Poznan, in Poland, Aston Villa topped their offer by £500,000 and the 24-year-old chose to accept the chance to move to the Premier League.
Tonev struggled to make any impact as Paul Lambert's side fought relegation, failing to score a single goal, and is now looking to kick-start his career again at Celtic Park.