Rangel, 79, announced he would temporarily step aside as the leader of the powerful tax-writing committee while an ethics investigation of him moves forward.
The leadership aide said Pelosi's decision to name Stark, an outspoken liberal, came during a Wednesday leadership meeting after Rangel's announcement, The Hill reported.
The House ethics committee announced Friday that Rangel violated gift rules by accepting paid travel to the Caribbean. Several Democrats earlier this week called upon the New York Democrat to resign his chairmanship.
By seniority, Stark was next in line for the chairmanship, but his personality led to some insiders wondering whether he would get the Ways and Means leadership post even temporarily, the Washington publication said.
Rangel sent a letter to Pelosi Wednesday in which he requested the temporary leave from the chairmanship, aides said.
Rangel declined to take questions during a short news conference Wednesday, saying, "I know that all of you have a professional obligation to ask questions."
Pelosi, D-Calif., said in a statement Rangel "informed me of his request for a leave of absence from his duties and responsibilities as chairman of the Committee on Ways and Means. I will honor his request."
Senate Democrats to pull all-nighter on climate change
Susan Sarandon 'very excited' about daughter's pregnancy