The Miami Herald said the announcement would be made official at a Wednesday news conference in Boca Raton.
Wexler, 48, is said to have accepted the position of director of the Center for Middle East Peace and Economic Cooperation, a think tank working to establish peace in the Middle East.
The Palm Beach (Fla.) Post described Wexler as a friend and political supporter of President Barack Obama and an ardent Capitol Hill ally of Israel.
Word of Wexler's planned resignation quickly sparked discussions in the heavily Democratic Boca Raton area over who would replace him. The Post said likely candidates for the special election included state Sens. Ted Deutch and Jeremy Ring and West Palm Beach Mayor Lois Frankel.