Ronaldo scored twice against Malmo in midweek – his 322nd and 323rd goals for the La Liga side, matching Raul Gonzalez’s record.
However, the club insist he has already broken the record, counting a deflected free-kick in 2010, that was later officially credited to Pepe.
Ronaldo was presented with a custom-made trophy, in front of his family and team-mates.
“It’s a very emotional day for all Real Madrid fans,” club president, Florentino Perez said.
“One of our own has achieved something that was considered almost impossible to achieve. Only through his talent, his hard work and his determination was this possible.”
Ronaldo, who has now netted a total of 501 career goals, said:
“To me it’s an honour to receive this award. I didn’t expect it.“When I wore Real Madrid’s jersey for the first time I never imagined that one day I would become the club’s greatest scorer, surpassing my friend Raul and the late [Alfredo] Di Stefano. I’m very happy.”