The 36-year-old re-joined his boyhood club for a third stint as a free agent, having left Turkish side Istanbul Basaksehir shortly after helping them win their first Super Lig title last season.
"I will play for a minimum wage, but the most important thing is to be here," Robinho told the club's official website on Friday.
"I am well physically and mentally, obviously there is still a little bit of rhythm [missing], but that over time we will gradually evolve."
He won two national championships, two Paulista tournaments and the Brazilian Cup in his previous two spells with Santos.
"I have many fond memories here," Robinho added. "The fans can be certain that I will give my best to help Santos FC on and off the pitch.
"Santos FC is going through a difficult financial time. So this is the time for those who can do something. I want to help the club that always gave me everything. Santos FC has already done a lot for me and this return is still little."
Santos are going through financial difficulties and could soon face a transfer ban from FIFA over unpaid debts.
Chilean club Huachipato are demanding Santos to complete the $3.4m deal over the signing of Venezuelan striker Jefferson Soteldo, while Colombian outfit Atletico Nacional claim they are still owed $774,000 from the sale of defender Felipe Aguilar.