The top seeded pair made a remarkable comeback to beat Russian second seeds Ekaterina Makarova and Elena Vesnina 5-7, 7-6(4), 7-5 in two hours and 25 minutes.
"Epic ladies' doubles final! So thrilled for @MirzaSania and @mhingis," 17-time Major champion Federer posted on Twitter.
This was also the Hyderabadi's maiden final at the All England Club across all senior formats though she had won the girls' doubles title here 12 years ago with Russia's Alisa Kleybanova.
Martina, on the other hand, has two women's doubles (1996, 1998) and one singles title (1997) to her credit that she won at the lone grass court Major. Saturday's trophy comes after a long gap of 17 years.
Indian author Chetan Bhagat also congratulated Mirza.
"Congratulations to #SaniaMirza for the amazing victory at Wimbledon! You inspire and make us all feel proud," he said.
Twitter was on Sunday with congratulatory messages.
"Congratulations to @MirzaSania for the thumping #Wimbledon2015 Women's Double with #MartinaHingis. Super Proud! #SaniaMirza," wrote Kalyanee Rajan, a Sania fan.
"Standing ovation to #SaniaMirza & My childhood icon #Hingis @MirzaSania @mhingis #Wimbledon #Wimbledon2015," wrote Chaitali Bakshi, another die-hard supporter of the two.