In 2005, former deputy prime minister John Prescott granted permission for the 22,500-seat stadium in Falmer, but consent was later withdrawn due to an error in the way the approval document had been worded.
Communities secretary Hazel Blears finally approved plans for the £44 million stadium in July this year.
Meanwhile inflation, coupled with the rocketing cost of raw materials such as steel, has meant that costs have risen by £9 million in almost two years.
However, the League One club has reassured fans that the hike in costs can be contained within the £50 million budget it has available.
The club has conducted a value engineering exercise and revised the stadium architecture to keep costs down.
Albion chief executive Martin Perry explained: “We have removed a floor from the original internal design. Those changes won’t affect the quality of the stadium at all and if anything the design will improve the stadium experience for supporters.”
The club has now invited construction firms to apply for the contract, which will be split into two stages, with building work due to start in September 2008.
The main construction contract for stadium and transport interchange is currently being advertised. Bidders are likely to include firms such as Bovis Len Lease, Alfred McAlpine, Laing O’Rourke and Sir Robert McAlpine.
Albion plans to kick off its 2010/11 season in the new stadium.