Mr Besigye, under house arrest since Friday, said Ugandans had seen "the most fraudulent electoral process".
He described the poll as a sham and a creeping military coup.
President Museveni, in power for 30 years, received nearly 61% of the votes, with Mr Besigye taking 35%.
Foreign observers say the poll was conducted in an atmosphere of fear and intimidation.
While praising the "remarkable determination" of Ugandans to vote, EU chief observer Eduard Kukan said the governing National Resistance Movement's "domination of the political landscape distorted the fairness of the campaign".
The election has been marred by sporadic violence and opposition allegations of electoral fraud, with social media sites and messaging apps blocked.
"Today I am under house arrest," Mr Besigye said in a statement.
"My home is sealed off and I am not allowed to leave. Nobody is allowed to access my home. I am also under some kind of electronic blockade. I am unable to access any form of internet service in my house.
"Generally, the regime is baring its bloodied fangs and claws for all to see. This has not been an electoral process. This is a creeping military coup."
It was the fourth time Mr Besigye, candidate for the opposition Forum for Democratic Change, had taken on President Museveni.
The two men were once allies, with Mr Besigye serving as Mr Museveni's personal doctor when they were guerrilla fighters.
He was placed under house arrest ostensibly to stop him announcing his vote score unilaterally.
Mr Museveni seized power in 1986 and is credited with restoring stability to Uganda. However, critics say he has become increasingly authoritarian.
The next closest challenger to Mr Museveni, former Prime Minister Amama Mbabazi, is also reportedly under house arrest.
The National Resistance Movement put out a statement celebrating the win, saying Mr Museveni's opponents had "failed to offer any alternative".
Uganda's old guard tries new election tactics
The main opposition leader in Uganda, Kizza Besigye, has rejected the result of Thursday's elections, in which President Yoweri Museveni won a fifth term of office.