The German club's boss has confirmed that the defender will move to the Serie A side before the close of the transfer window, with a deal likely to be completed as late as Monday
The Denmark international has been strongly linked with a move to the Serie A side as they seek a replacement for Philippe Mexes, who left the club for AC Milan earlier in the summer.
Kjaer revealed earlier on Thursday he had been granted permission to leave, and Magath has indicated the defender will join the Italian capital club.
"He is on his way to sign a contract with Roma," Magath said after Thursday's training.
Wolfsburg have not commented on the figure involved in the transfer, but recent reports have suggested Roma are willing to pay as much as €10 million (£8.8m) for the defender, who joined the club only last summer.
Kjaer's time at the Volkswagen Arena has been met by frustration, as the club narrowly avoided the drop last season and he has come under fire for some lacklustre displays.
The 22-year-old centre-back appears set to accept a second spell in Italy, after playing at Palermo from 2008 to 2010.