In a message posted on his blog: "My warmest and heartiest congratulations to A.R. Rahman and Resul (Pookutty) for winning recognition in music and sound and to Gulzar for co-assisting Rehman in the lyric category."
While Rahman bagged an individual Oscar for the best original score for the Danny Boyle-directed film, the ace composer shared the honour with Gulzar for their song "Jai ho" featured at the end of the film.
Pookutty was awarded the golden statuette for the best sound mixing for the film.
It is for the first time in the history of the Academy Awards that three Indians have won the Oscar - considered the penultimate award in global cinema. The film won eight Oscars.
"International recognition for Indian film talent on one of the most well known and popular forums - this is the happiest day for Indians and the industry," said Amitabh.
Earlier, Amitabh had stoked a controversy by slamming "Slumdog Millionaire" as a film that "projects India as the Third World's dirty underbelly developing nation and causes pain and disgust among nationalists and patriots".
The film, based on Indian diplomat Vikas Swarup's novel "Q&A", stars British Indian debutant Dev Patel and actress Freida Pinto in the lead, apart from Anil Kapoor and Irrfan Khan in pivotal roles.