Nemes Tarimo was serving a seven-year term for an undisclosed offense.
Russia's Wagner mercenary group recruited him for payment and the promise he would be freed after the war, Tanzanian authorities said this week.
Following his death on October 24, his body arrived in Tanzania on Friday, with tearful family members gathering at the Julius Nyerere International Airport in Dar es Salaam to receive his remains.
The short memorial service was attended by government officials as well as representatives from the opposition Chadema party, which counted Tarimo among its members.
In a eulogy, a family member said Tarimo was father to a three-year-old girl who was still in Russia.
After prayers, mourners lined up before the closed coffin, which had a framed photograph of Tarimo.
"Due to circumstances which are out of our control, we will not display the physical face of the late Tarimo," a relative told mourners.
Tarimo's uncle Dickson Muro said he spoke to the student last year.
"Tarimo called me and said he was free and promised to return home this January. He also warned that I should not call him until he does so," he said.
Tarimo's stepfather said the student had told him he had secured a job in Ukraine.
"I told him to be careful there because of war, but he told me not to worry," said Sultan Nassoro.
Chadema official Ernest Mgawe said Tarimo had bid for the party's member of parliament nomination in Dar es Salaam in 2020.
"We lost a commander," he said.
Tarimo's body will now be buried to the southern region of Mbeya.
In recent months, men have been recruited from Russian prisons to fight on the front lines in Ukraine with the promise of lucrative wages and reduced sentences.
Zambian student Lemekani Nyirenda, 23, was killed in Ukraine in September, triggering a diplomatic spat and prompting Lusaka to demand an explanation from Moscow.