He was estranged from his wife of six years, Rebecca Metcalfe, and leaves a 2-year-old son, Jack.
A statement on behalf of his family said: "Lee was lovely. He would do anything for anybody, he always looked after his sisters and always protected them. He took a 'big brother' role with everyone.
"All he wanted to do, from when he was a little boy, was to be in the Army. He wanted to live life and enjoy himself. His family meant everything to him. He was a loving son, husband, father, brother and uncle, and a friend to many.
"We ask that our privacy be respected at this difficult time."
Rigby's colleagues from 2nd Bn The Royal Regiment of Fusiliers described him as one of its "great characters". Lieutenant-Colonel Jim Taylor, the commanding officer of the Second Fusiliers, led tributes to the "dedicated and professional soldier", a talented parade drummer who performed outside the royal palaces and whose strong personality marked him out to work in Army recruitment.
"He was a real character. Larger than life, he was at the heart of our Corps of Drums. An experienced and talented side drummer and machine gunner, he was a true warrior and served with distinction in Afghanistan, Germany and Cyprus.
"His ability, talent and personality made him a natural choice to work in the recruiting group."
Rigby, who was better known to his colleagues as "Riggers", joined the army in 2006 before being posted as a machine gunner in Cyprus. On his return to Britain in 2008 he played a central role in his battalion's public duties, which included parading outside the royal palaces. In April 2009, he was sent on tour of Helmand province, Afghanistan, where he served as a member of the Fire Support Group at the Patrol Base Woqab.
He completed a second tour of public duties with the battalion in Celle, Germany, before returning to Britain in 2011 to take up a recruiting post. He also assisted in duties at regimental headquarters in the Tower of London.
Sergeant Barry Ward, Drum Major in the Second Fusiliers, said: "Drummer Rigby was a loving father, with a very bubbly character."
Rigby married Metcalfe at St Anne's Church, in the village of Southowram, West Yorkshire, in 2007.
His former brother-in-law said "he died in the most horrific way".
The Rev Guy Jamieson, who married the couple at St Anne-in-the-Grove Church, near Halifax, described Rigby's death as an "absolute tragedy".
"It's abhorrent. We hear a lot about military tragedies overseas but the fact that it was in the street in a city makes it more horrific.
"I remember his wedding well. He had already spoken to the chaplain at Catterick [Garrison] and came to me well prepared with lots of questions. The wedding day was wonderful.
"Because it was a military wedding it requires a lot of preparation. I remember sitting next to Lee on the front pew before everything started and reminding him what his first words to say were."
