The first-term Republican representing southern Florida was to announce his resignation in a letter to House Speaker John Boehner, a Radel spokesman told AFP.
Radel, 37, was arrested in October after he was caught purchasing 3.5 grams of cocaine from an undercover police officer outside a Washington restaurant.
He faced a maximum penalty of 180 days in jail, but instead was sentenced to one year of supervisory probation.
Radel spent nearly a month at a rehabilitation facility. After his leave of absence he had said he aimed to continuing serving in the House of Representatives.
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"Sometimes in life you need a wakeup call. This is my wakeup call," he said in November before undergoing rehabilitation.
Radel's term ends in January 2015, and he would have stood for re-election this November.
His departure triggers a scramble for the open seat, with speculation that Radel's predecessor, Connie Mack, who held the position before an unsuccessful run for the US Senate, might seek to reclaim the seat.