The Islamists, including the head of the Harkat-ul Jihad Islami group, were sentenced to death in 2008 for the attack in which three people were killed and about 50, including then British High Commissioner Anwar Choudhury, were wounded.
A panel of four judges headed by Chief Justice Surendra Kumar Sinha upheld the death sentences for the three, including the group's leader, Mufti Abdul Hannan, Deputy Attorney General Bashir Ahmed told reporters.
The court also upheld life imprisonment for two others for the May 21, 2004, attack, he said.
Defence lawyer Mohammad Ali told reporters he would file petitions seeking a review of the court's judgement.
The attack came after Friday prayers at a Muslim shrine in the northeastern district of Sylhet. The Bangladesh-born British envoy was wounded in the leg.
The militant group was blamed for several other attacks, including a bomb blast later in 2004 on a rally by Prime Minister Sheikh Hasina, who was then the leader of the opposition.
Twenty-three people were killed and more than 150 wounded in that attack. Hasina suffered partial hearing loss.
The ruling came amid rising concern over the growth of Islamist militancy in the Muslim-majority South Asian country of 160 million people, which has seen a string of deadly attacks recently, the most serious on July 1, when gunmen stormed a cafe killing 22 people, most of them foreigners.
