Montanella has been capped once by France against the All Blacks in 2007, while Joly has represented his country at U19 and U20 level.
"They're both very experienced in the French leagues, which is a tough environment for front-five forwards," said London Welsh head coach and former Ospreys boss Lyn Jones.
"They're both good scrummagers and they carry well - they'll give us some much needed bulk.
"With Franck and Arthur on board, as well as Paulica Ion and the boys we've kept from last year, our front row is capable of competing in the Aviva Premiership."
Weighing 125kg, Montanella is a well-respected scrummager and a big ball carrier who has had spells with Stade Francais, Narbonne, Strasbourg and Auch after beginning his career with home-town side Racing Club Cannes-Mandelieu.
The 30-year-old won his solitary French cap came back in 2007, at a time when he was playing second division rugby with Auch.
Joly, who is still just 24 and weighs in at 122kg, started off with Massey before spending four seasons at Stade Francais. He joined Bourgoin in 2011 and is now the latest addition to head to Old Deer Park and the Kassam Stadium for the Exiles' first Premiership campaign.
The news is a timely boost for Jones and co after Wales international Gavin Henson fractured his cheekbone at the Scarlets last weekend - a game that saw Montanella and Joly both make their debuts.
Henson is expected to be out of action for six weeks, starting with Saturday's Premiership opener at home to Leicester.