Malbranque, who was a free agent after leaving Saint-Etienne last year, returns to the Stade Gerland after spending 10 years in England with Fulham, Tottenham and Sunderland.
Argentina international Monzon arrives from Ligue 1 rivals Nice for a fee of three million euros.
Les Gones president Jean-Michel Aulas told olweb.fr: "Steed returns to Lyon after many years in England. He has signed for one season.
"Fabian arrives from Nice on a four-year deal for three million euros.
"I am delighted to welcome these two players."
Malbranque only made one appearance for St Etienne despite signing a two-year deal last August, agreeing to a mutual termination of his contract one month later for undisclosed reasons.
The 32-year-old said: "I've come home and I'm very happy to do so. Lyon is a club close to my heart.
"The challenge of getting back to a high level after 10 months out is exciting.
"I want to show everybody that I still have the desire and determination.
"I hope that everything goes well and we have a good season. I'm not apprehensive.
"I really want to repay the club."
Monzon, 25, added: "I'm very happy to be at Lyon where everybody has welcomed me."
Despite marshalling Nice's backline last season, the centre-back registered 10 goals as the club's appointed penalty taker.
