It is one of the first marine renewable energy projects to be approved in the UK and follows the recent launch of the £10 million Saltire Prize.
First Minister Alex Salmond said: "Today's announcement is a significant step in Scotland's journey to become a world leader in renewables. The Siadar wave farm will be one of the largest consented wave electricity generating station in the world. It is the first commercial wave farm in Scotland and is starting with a capacity to power around 1,800 homes.
"This is good news for the Western Isles and for Scotland but its long-term potential is global. I wish power the very best in the development of this innovative wave farm."
SNP MSP Alasdair Allan and MP Angus MacNeil welcomed today's announcement.
Mr Allan commented: "I am delighted that the Scottish Government have decided to grant planning permission for this innovative and exciting renewable energy project for the west coast of Lewis. This project has been driven and supported from the beginning by the community, and comes at a time when the Western Isles needs work."
Western Isles MP Angus MacNeil stated: "This ground-breaking proposal will not only produce enough energy to power around 1,800 homes and provide some very welcome jobs on Lewis but will also provide an 'active' breakwater for the communities in and around Siadar.
"This approval is testament to the hard work of all those in Lewis who have worked to get this project off the ground, and I believe that the right decision has been made by the Scottish Government today."