Greenwood was suspended in January 2022 by Manchester United following allegations of attempted rape and sexual assault but prosecutors dropped charges in February 2023.
Marseille fans, including the city's left-wing mayor Benoit Payan, condemned the signing.
"I understand the question, but I don't really want to get into any conversations or any discussions about that," he said.
"I'd only like to look forward and to be part of Marseille and just to move forward with myself, my family, my daughter and my partner and the whole club and to focus on the football and the off-field work with my family."
Greenwood spent last season on loan at Getafe in Spain's LaLiga. Marseille paid Manchester United a reported 30 million euros ($32.7m) for the forward.
"I'm the first to understand that Mason's arrival raises a lot of questions," said Marseille president Pablo Longoria. "But we're talking about the past.
"It's a complex situation and an old situation," Longoria said.
Greenwood scored 10 goals and provided six assists in 36 games for Getafe last season.
"In my personal life, I was in Madrid last season which was very good with my partner and my daughter. We lived very comfortably in Madrid and were all happy."
The English striker could start in Marseille's first friendly of the season against Nimes on Sunday.
"On the right is my preferred position but it's up to the coach to pick me in whatever position and I'll give 100 per cent in every single game," said Greenwood of his role on the team.
Greenwood has played once for England. Asked whether playing at Marseille could lead to an international recall, he said he wanted "to concentrate on my club football this season".
His arrival in Marseille comes the day after the official departure of Pierre-Emerick Aubameyang, the Gabon international who was Marseille's top scorer last season.
His arrival in Marseille comes on the week that Pierre-Emerick Aubameyang, the Gabon international who was Marseille's top scorer last season, left for a club in Saudi Arabia.
