As required by the constitution, Mr Buhari has written to MPs to say he is back in charge, he tweeted.
His absence caused concern and on getting back home he told dignitaries he had never before felt "so sick".
However, he made no disclosure as to the nature of the illness which had kept him away from his office.
The president appeared frail when on Friday he stepped off the plane which had brought him back from London.
He proceeded to deliver a nine-minute statement saying he deliberately came back towards the weekend "so I will continue to rest".
He said further medical checks would be required.
"I have resumed my functions as the President of the Federal Republic of Nigeria with effect from Monday," a statement released by Femi Adesina, Mr Buhari's special adviser, quotes him as saying.
Vice-President Yemi Osinbajo had been in charge throughout Mr Buhari's sick leave.
It was the second time in less than a year that Mr Buhari, who won elections in 2015, has sought medical assistance overseas.
Last June, he spent nearly two weeks, again in London, for treatment for an ear infection.
Nigerian President Muhammadu Buhari has resumed his duties three days after returning home from a medical leave abroad.