Mr Osinbajo cited Burnaboy and Wizkid for taking the entertainment industry by storm and winning the Grammy Awards.
The Nigerian leader issued a laundry of press releases signed by his spokespersons.
The congratulations comes amidst rumours of simmering feud among trio, causing a surprise among fans of the superstars.
‘Twice as Tall’ did not win as much applause in Nigeria, but Burna knew exactly where he wanted it to reverberate. And yesterday, the sound was affirmed.
“We celebrate Nigeria music afrobeat stars Damini Ogulu @burnaboy and Ayodeji Ibrahim Balogun @wizkidayo on their #GrammyAwards. The best is yet to come.”
Central to the music are vocals, complex intersecting rhythms, and percussion, popularised by multi-instrumentalist and bandleader Fela Kuti.
The victory was announced on Sunday evening (Nigerian time) at the 63rd Annual Grammy Awards premiere.
