"I just thought he's a good player and he can play several positions for us, he can play in a midfield or attacking-midfield role if we want to change our system," manager Harry Redknapp told the BBC on Thursday.
"We've lost Aaron Lennon (to injury) so we haven't got a great deal of width. We can play a diamond formation if we want to and he can be a big player in that system.
"So, yes, we took him on loan until the end of the season to see how it goes."
Gudjohnsen was due to have a medical at the north London club before finalising the deal this week.
The Iceland international has played 11 matches in all competitions for Monaco this season, starting seven, but has not scored for the Ligue 1 side.
The 31-year-old had also been a target for Tottenham's heavily-indebted Premier League rivals West Ham United, who hope to bring in two new strikers in their fight against relegation.
"We thought we had a deal and the player had even had a medical," West ham co-owner David Sullivan told the BBC earlier this week. "We then heard that Tottenham were trying to speak to the player.
"I can't say I am happy about it but I believe in karma and what goes around, comes around."
Redknapp was quoted in the London Evening Standard on Thursday saying: "We've been talking about Gudjohnsen for nearly two weeks and when we heard West Ham were interested we made our move.
"We are not paying a penny more than West Ham were offering him. Two identical deals were on the table. In the end it was a straight choice for the player."
Tottenham, who are fourth in the table and fighting for a Champions League slot, also said on their website that their Mexico midfielder Giovani Dos Santos had joined Turkish side Galatasaray on loan until the end of the season.
