The actors have starred in three feature films together, including blockbusters Bajirao Mastani and Padmaavat.
Forbes Magazine reports that the couple made an estimated $21m (£16m) in combined earnings last year.
The wedding happened on Wednesday, which was the anniversary of the 2013 release of their first film together – Goliyon Ki Rasleela Ram-Leela.
Although reporters were not invited for the event, images of the pre-wedding ceremonies made their way to entertainment magazines and newspapers.
People have been keeping a sharp eye out for pictures that may be shared by careless guests on their social media accounts – the couple had reportedly banned guests from posting anything about their wedding.
One image – shared by singer Harshdeep Kaur was briefly up on Instagram. She deleted it, but not fast enough for screenshots to start circulating among an information-starved public.
Details – such as the fact that Singh got on one knee and made an impassioned speech to his future wife, and that the couple have asked guests to donate to Padukone’s mental wellness foundation in lieu of wedding gifts – are also being passed around frantically.
Rumours that the actors were dating each other were circulating for six years, but they did not officially confirm their relationship until earlier this year.