Nearly 20,000 solar panels will be installed across three fields on farmland in Gisburn following the decision at a meeting on Thursday.
The scheme was opposed by some local residents and Ribble Valley MP Nigel Evans, who said it would damage the rural landscape.
Developers Island Green Power say their plans will provide clean energy.
Spokesman Mark Dickinson said: "Naturally we are very pleased and we looked at a huge amount of sites nationally."
He acknowledged that the farm will have a "minor visual impact" but said they had to get things into perspective as it was a "new technology that is not destructive, recyclable and temporary."
Mr Dickinson said Island Green Power were not interested in any other sites in the Ribble Valley.
Local resident Helen Heslop, who opposed the plan, said she was "really disappointed" by the council's decision and that the outcome "seemed to be a foregone conclusion".
Another protester, Graham Hardman, said he had received a lot of support and was extremely disappointed.
There was "no chance of an appeal", he added.
Plans for a large solar farm in Lancashire have been approved by councillors in the Ribble Valley.