Matthews said he was leaving his post to spend more time with his family and decompress from planning for the Super Bowl.
During Wednesday's meeting, council members praised Gillmor's ability to lead and committed themselves to clashing less and collaborating more. The six current members of the council, including Gillmor, have often split 3-3 on issues related to the stadium, the 2-year-old home of the San Francisco 49ers.
Councilman Dominic Caserta has been Gillmor's biggest adversary, but he indicated there will be a change after the City Hall upheaval.
"I really believe this is an opportunity for us to come together, and I believe Lisa can lead us in doing that," said Caserta.
As Gillmor takes over as mayor, there is an ongoing Santa Clara County civil grand jury investigation of the city's Stadium Authority, the agency that oversees Levi's Stadium.
The mayor, city manager and council members are all members of the authority. Both Gillmor and Santa Clara's city attorney have declined comment on the grand jury investigation.
But Gillmor stressed her top priority is to propose an independent audit to make sure Santa Clara is in compliance with a city ordinance, Measure J, that prohibits the use of public funds for security at Levi's Stadium.
"I'm very concerned about that as are many citizens of our city," said Gillmor.
The 49ers would not comment on the security question but issued a statement saying, "We enjoyed working closely with Mayor Gillmor to make Levi's Stadium a reality during her tenure as a council member and look forward to continuing to work with her on stadium-related matters."
Gillmor also plans to change the relationship with the management of the 49ers who, she said, often deal with city officials in closed-door sessions. The City Council may soon consider a proposal that could lower 49ers' rent payments on the stadium.
"There's going to be a lot more discussion, a lot more interactions, a lot more community exposure to what's happening," said Gillmor. "I think that communication will definitely improve with the 49ers."
Gillmor also said she wants to make the planning process for proposed development projects around Levi's and Santa Clara University more transparent.
"I think that there's been a lot of discussions that are not taking place in public. I'm not saying anyone has done anything illegal, I'm not saying anything like that," said Gillmor. "It's just that we are probably a little deficient in our public outreach."
Gillmor was appointed to the council in 2011 to fill Matthews' seat when he became mayor. She was elected in 2012. The process to fill her seat will begin shortly.