The Brazil winger will cost Chelsea £30m from Real Madrid and give Luiz Scolari an potent option on the wing.
Subject to a successful medical, the player will train with his new colleagues on Thursday and will be in the squad for Sunday's derby against Spurs at Stamford Bridge.
Robinho has been Chelsea's chief target all summer and the protracted delay in signing him could have hampered Chelsea's opening Premier League campaign.
But the Blues have registered successive victories and sit top of the table.
Chlesea plan to recoup at least £9m from the sale of Shaun Wright-Phillips to Manchester City with 48 hours.
SWP cost Chelsea £25m.
Chelsea ditched Andriy Shevchenko back to AC Milan on loan and he is likley to be granted a free transfer next season. He cost Chelsea £30m just 30 months ago.
Sheva took a pay cut to rejoin Milan.