The Shoreham footbridge, which will link the two sections of the town over the River Adur estuary, will cost £9.8m instead of the estimated £5.8m.
Construction was supposed to have started in the spring, but will now get under way at the start of August.
The bridge is expected to take 45 weeks to complete and open to the public in the summer of 2013.
Funding has come from West Sussex County Council and sustainable transport charity Sustrans, which received a £50m grant from the Big Lottery Fund to extend the National Cycle Network.
The work was delayed to allow a review of the project by the council and the main contractor, Osborne.
Peter Wanless, chief executive of Big Lottery Fund, said the bridge would encourage people to make journeys on foot or by bike instead of by car.
Work to build a West Sussex footbridge which was delayed after the cost nearly doubled is to begin later this summer.