The retail development is for a 2ha garden centre comprising 9,725m2 of retail space and parking and landscaping.
East Lothian Council's planning committee had turned down an application in October amid fears of the effect the garden centre could have on town centre businesses.
The shop area is 2,443m2, a cold glasshouse of 345m2, an open-sided canopy of 833m2 and an open sales area of 6,104m2. Car parking for 169 cars plus coaches. Planning advisor is Malcolm Scott Consultants.
Crabbie said that "common sense" had prevailed.
More than 40 full-time, part-time and casual jobs will be created at the centre - which will have an estimated turnover of £2.5 million by 2012/13.
An estimated six per cent of the trade diversion caused by the centre would affect Dunbar town centre - a retail impact of 2.6 per cent - with "very small proportions" affecting North Berwick and Haddington.