"He is a player that we followed for a long time, since he played in the Serbian Under 21 side in the European Championship," Grant told Chelsea's website.
"When he played in Moscow, I saw him there also. He is a good player for now and also for the future because he is very young and can play in many positions on the pitch - and I welcome him.
"He hasn't trained for many weeks because the Russian league finished and he is not in the squad for the moment."
Ivanovic's last full game was in the first week in December. He joined Chelsea's training regime full time last week and the 23-year-old is working hard to catch up with his new team-mates.
"I was training a lot on my own before coming here, but that is not the same as training with the team,' explained the player who has experience playing right-back, centre-back or defensive midfield.
"I will try to reach my potential and then it is up to my coaches to decide what is the best position for me.
"It is up to me to raise my level to the standard at Chelsea and I am trying my best to reach that level as soon as possible and to learn from them."