Anderson, 23, impressed for Nottingham Forest last season, scoring four goals and adding four assists in 38 league appearances, 37 of which came as starts.
The England international was officially confirmed as a Manchester City earlier this week after completing his transfer away from the City Ground, bringing an end to speculation over his future.
He is currently away on international duty at the World Cup, where he has featured in all four of England's matches so far and registered one assist along the way.
Anderson operates in central midfield alongside Rice, 27, who plays his club football for Arsenal, and the pair have quickly struck up a strong understanding while on England duty together this summer.
"He is one of the best I have played with. He is constantly involved in the game, he is the engine of the team," Rice said, according to journalist Fabrizio Romano.
"Our first nine, ten months together have been fantastic."
Rice's praise will come as a welcome endorsement for Anderson as he prepares for the step up to one of the Premier League's leading clubs.
Anderson's price tag has been the subject of considerable attention this summer, with The Athletic reporting last week that Manchester City paid £116million to sign him.
That fee comfortably eclipses the £100million plus £5million in add-ons that Arsenal paid West Ham United for Rice when he completed his own move to the Emirates Stadium.
Rice was quick to point out that Anderson bears no responsibility whatsoever for the scale of his fee, just as he had none over his own valuation when he left West Ham for Arsenal.
"I couldn't control what I went for, he can't control what he goes for," Rice said, again according to Romano.
The comments underline the esteem in which Anderson is already held by senior England teammates as he begins the next chapter of his career at Manchester City.