The marriage itself is set to take place marry on Friday in a traditional Hindu ceremony.
Crowds of fans strained for a glimpse of the stars outside the two seaside residences of the Bachchans, as well as outside Rai's home.
"I've been waiting for two days (to see the pair)," said 26-year-old fan Ramakant Shukla, a waiter who travelled from the eastern Indian city of Patna to Mumbai's entertainment capital for the celebrations.
Unlike usual Indian weddings where the guest list can run into thousands of people, the Hindu ceremony late on Friday will be restricted to close friends and family out of deference to Bachchan's grandmother, who is ill in hospital and reported to be very keen to see her grandson wed.
The ceremonies kicked off on Wednesday with elaborately choreographed song-and-dance routines at the Bachchan residence and bride-to-be Rai was reported to have returned home in the early morning hours.
Only 100 guests have been invited to the wedding, and more than 500 police are expected to be on hand to keep out gatecrashers, according to media reports.
The local post office reported that fan letters and gifts were flooding in for the couple from across the country, and even from as far away as London and New York.
"It has been a tough day today and the mail is pouring in," said postman S. Shinde. "We expect more."
The three-day wedding ends with a traditional parting of the bride from her parents.
The pair have starred together in at least five movies and are seen as a dynamite box office duo.
Bollywood movies have a huge following around the world, especially in nations with a large Indian diaspora such as Britain, Malaysia, Singapore and South Africa.
The couple known as "Abhiash" -- India's answer to Brad Pitt and Angelina Jolie's "Brangelina" -- were engaged in January.
Huge efforts have been made to keep the festivities private and to exclude the media.
The Bachchans have asked owners of neighbouring buildings not to allow photographers crews to shoot pictures from roofs while the gates of Bachchan's residence are now mirrored so fans trying to peer inside would see only their refection -- in line with an Indian custom to ward off the evil eye.