As part of the deal the Reds have negotiated a buy-back option for each of his first three seasons at Rosenborg.
Rosenborg's sporting director is former Red Stig Inge Bjornebye, who believes the youngster is the perfect fit for their fluent style.
Chirivella, who had two years left on his Liverpool contract, made five first-team appearances for the club.
During his time on Merseyside the midfielder, dubbed by some 'the next Xabi Alonso', had loan spells at Go Ahead Eagles and Willem II.
Rosenborg's sporting director Stig Inge Bjornebye spent eight years at Anfield (Image: GETTY)
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Players Out: Ovie Ejaria (Rangers, loan), Emre Can (Juventus, free), Jon Flanagan (Rangers, free), Jordan Williams (Rochdale, free), Adam Bogdan (Hibernian, loan), Harry Wilson (Derby, loan)