The 35-year-old center revealed at the end of last season he is gay, but he was a free agent and had remained unsigned.
Collins was aware of the magnitude of his signing, but repeatedly said he was most concerned with learning the Nets' schemes.
"Right now I'm focusing on trying to learn the plays, learning the coverages and the game plan and the assignments. So I didn't have time to really think about history," Collins said at a crowded news conference less than an hour before tipoff.
"The pressure is playing in an NBA game tonight and last time I played in an NBA game was last April," Collins said. "So I think that's enough pressure right there."
With a need for another big man, the Nets turned to the 7-foot Collins, who helped them reach two NBA Finals in the early 2000s.
"The decision to sign Jason was a basketball decision," general manager Billy King said in a statement. "We needed to increase our depth inside, and with his experience and size, we felt he was the right choice for a 10-day contract."
The Nets are owned by billionaire Mikhail Prokhorov of Russia, where a law banning so-called gay "propaganda" was the subject of protests and controversy at the just-concluded Sochi Winter Games.
Collins has played 12 NBA seasons, including his first seven with the Nets, when they were in New Jersey and Jason Kidd was their point guard. Kidd is now the Nets' coach and Collins has been a teammate of several other current Nets.
"Jason told us that his goal was to earn another contract with an NBA team. Today, I want to commend him on achieving his goal. I know everyone in the NBA family is excited for him and proud that our league fosters an inclusive and respectful environment," Commissioner Adam Silver said.