Francois Blais was sworn in as education minister on Friday, moving over from employment and social solidarity.
Bolduc quit politics on Thursday in the wake of a number of scandals, including recent comments about strip searches at Quebec high schools.
Blais, a former dean of social sciences at Laval university, will also take on the task of the higher education portfolio.
His former cabinet post will be absorbed by Labour Minister Sam Hamad, while Natural Resources Minister Pierre Arcand will take on another of Bolduc's responsibilities as minister in charge of province's Cote-Nord region.
Couillard also said Friday he's uncomfortable with the idea that Bolduc would accept a $152,000 transition allowance.
Although common over the years, the allowance designed to help politicians transition back to private life has increasingly come under scrutiny.
Two opposition members of the legislature who quit in recent months both renounced their right to the severance.
Couillard said the final decision is up to Bolduc, who is returning to practise medicine.
A 2013 report suggested Quebec politician salaries be raised while eliminating such bonuses and discretionary allowances.
Couillard said all politicians must work together on the issue.
"We also believe this should stop, but there is only one way it can stop," Couillard said. "But there's only one way it can stop: if we do it piecemeal each time there is a case, we'll never solve the issue."Suggest a correction