The 41-year-old moves across Lancashire from Preston, where he was working as head of youth development having called time on a professional career spanning more than 1,000 games at the end of last season.
Alexander replaces Micky Mellon in the Highbury Stadium hotseat and is taking on a first senior management role with the npower League Two club.
He guided North End for five games last term alongside David Unsworth in a caretaker capacity before Graham Westley's mid-season arrival.
Despite leading Fleetwood to two promotions in the past three years and currently seeing them occupy the final League Two play-off spot, Mellon was sacked in the wake of last weekend's FA Cup second-round defeat to
Aldershot - the Cod Army's third consecutive loss in all competitions.
Alexander's first game at the helm comes on Saturday at home to fellow promotion-chasers Southend.