Williams said he made the decision to come back in February, but answered, "I don't know" when he was first asked why he was coming back to football.
Williams later acknowledged that money played a role in his decision. He's still facing an $8.6 million judgment in favor of the Dolphins and also has to pay child support for his three children.
"Looking at the future, I have that settlement chasing me," William said. "I can't say that didn't play in my decision."
Williams' agent, Leigh Steinberg, confirmed that Williams' current salary is the league veteran minimum of $540,000. Williams initially was slated to make $3.7 million thanks to contract "escalators" he had reached, but those disappeared after he walked away from the team.
Steinberg said he had plenty of time to address Williams' contract situation with the team, but that Williams returning and reconnecting with his teammates was the priority for the time being.
"We're trying to put his life into a more productive path," Steinberg said. "This is an enormous first step he just took."
Williams said his biggest goal right now was to "not let all the outside stuff be a distraction."
For his part, head coach Nick Saban made it clear he didn't want to discuss Wililams' return after today.
Saban directed reported to limit their questions about Williams to things pertaining to "today and on."
Williams asked Saban to address his teammates after reporting on Sunday and Williams apologized to them as well.
But Williams was happy with the reaction he got from his teammates.
"It was surprisingly positive," he said. "I could tell a lot of guys care about me and are happy I'm back."