The easiest and most convenient way to store your luggage is to leave it in your hotel. If you already checked out, the receptionist, the concierge or the luggage porter might take it. A small fee might be advisable as a tip to please them.
If luggage storage in the hotel is not available or you simply want to be on the safe side, there are official offices available to store your suitcases. The Marco Polo airport offers luggage storage near the post office in the arrival hall.
Also in the St. Lucia Railway station the deposit of luggage is available, located near track 1.
Additionally luggage can be stored at the Venice Cruise Terminal. The offices are available in the Marittima and San Basilio buildings.
Another option is the Piazzale Roma where a deposit office is available to the public.
Finally there is a luggage deposit in the historic center of Venice, San Lio (Calle della Malvasia, among Salizada San Lio and the Church of Fava), in the vicinity of San Marco and the Rialto. It is open 9.30 AM to 19.30 daily and costs from 6 € for first piece, then 5 € for second piece. For more information see this page.