The 29-year-old completed a medical in the French capital on deadline day but an agreement between the clubs was only reached in the last hour of the January transfer window.
The Morocco international has been trying to leave west London for over six months after falling out of favour under Thomas Tuchel and has since failed to fully reclaim his place under Graham Potter.
After a successful World Cup in Qatar, Ziyech had the attention of several sides including AC Milan, Roma, Newcastle and Everton.
He has, however, opted to move to France’s biggest club although the loan does not include a purchase option, so any future fee must be agreed upon at a later date.
Chelsea waited until the end of the transfer window to release Ziyech due to an injury crisis that left as many as 12 players on the sidelines at its worst point.
However, with many players on their way back to fitness ahead of Friday’s match against Fulham, the Blues opted to allow Ziyech to leave.
It follows eight January signings including four attackers; Mykhailo Mudryk, Noni Madueke, Joao Felix and David Datro Fofana.
Chelsea have made an unprecedented splash in the market, spending over £550million of talent acquired after Enzo Fernandez agreed a British transfer record deal on deadline day.
