Sir Tony gave a Bible reading, while Mr Dromey’s daughter Amy Harman read an extract from her mother’s book A Woman’s Work.
Some had tears in their eyes as they entered the church just before noon, with Cabinet ministers, broadcasters and Labour MPs in attendance.
The father-of-three, who had represented Birmingham Erdington since 2010, is understood to have died from natural causes.
Born in London in 1948, he had three children with Ms Harman, the former deputy Labour leader, who announced last month she will stand down as an MP after the next general election.
They married in 1982.
Mr Dromey joined the Labour frontbench as shadow housing minister in 2010 under then-leader Ed Miliband, who was also at the service.
Jess Phillips, Labour MP for Birmingham Yardley, told the PA news agency: “It was brilliant and funny and beautiful and a testimony to Jack.
“I just felt very much that Harriet and Jack will be very proud of their children who stood up very bravely and gave brilliant testimonies.”