Marquez, 56, will have to give up a number of posts on area boards before taking office.
He is expected to step down from the Chino Valley Independent Fire District board as well as the California Special Districts Association's legislative and finance committees.
He may also have to resign from the California Institution for Women advisory board and the Carbon Canyon Fire Safe Council.
According to the California Government Code, a public officer, including, but not limited to, an appointed or elected member of a governmental board, commission, committee or other body, cannot simultaneously hold two incompatible public offices.
Marquez said he plans to visit with city officials to find out if he can continue to be involved with the Fire Safe Council and CIW board.
Tuesday's special election needs to be certified before Marquez surrenders the Fire District and Special Districts Association positions.
"I talked to the city attorney and right before I get sworn in I would resign from those positions," he said.
The San Bernardino County Registrar of Voters said his office plans on certifying the election by Friday.
Marquez could then be sworn onto the City Council as soon as Monday or at the next council meeting on Tuesday.
Marquez, a retired firefighter and a real estate broker, became a Fire District board member in 2006 and has volunteered with the Special Districts Association's legislative and finance committees for five years.
"The board will have to get together and chart out the best course on how they'll fill that vacancy," Fire District spokeswoman Massiel de Guevara said.
Officials at Special Districts Association said that when Marquez notifies them of his resignation they'll remove him from both committees.
"When someone leaves we leave the committee the way it is," said Charlotte Lowe, executive assistant for the Special Districts Association.
"We ask for volunteers for committees every year, once a year, (in August). The committee only makes recommendations to the board - that's all their action is. The board will have final approval on the recommendation. It's not too formal - it's just on a volunteer basis."
Independent agencies range in size from small to very large and often cross political boundary lines, such as city and county borders, to serve a common community of interest, according to the association's website.
The Registrar of Voters Office showed Marquez finishing first among four candidates with 45 percent of the vote.
Debra Hernandez, Rossana Mitchell and Jesse Singh also ran to succeed Bill Kruger, who resigned from the council in September.