Centre Mordt arrives at Vicarage Road after spells with London Irish, Northampton and Harlequins, winning international honours with England Saxons and England Sevens along the way.
Loosehead prop Parr returns to the top flight from Nottingham, having previously played for Sale and Leicester.
Zimbabwe-born Mordt is looking forward to the challenge of trying to help Sarries go one better than their heartbreaking Premiership final defeat against Leicester at Twickenham on Saturday.
"I believe it might have been said before," he said, "but there is something special happening at Saracens, and I want to be part of it."
Director of rugby Brendan Venter said: "I have known Nils for some time, and he has great hands and fantastic natural ability. He's also an outstanding character, and I'm sure he will thrive in our environment."
The 27-year-old Parr added: "Petrus du Plessis moved from Nottingham to Saracens a couple of months ago, and has done really well, so I'm looking forward to following the same path. Anybody who has watched Saracens over the past few months can see there is something happening at the club... and, you know what, it's special."
Venter added: "Matt has been highly recommended to us, not least by his front row team-mate Petrus, and we are confident we have found another gem in the Championship.
"We are not a club that trawls the who's who of world rugby - we look for players with talent and character, and that's exactly what we have signed in Matt."