The club plans to develop a 73,000m2 area across the River Calder from the existing facility.
Further proposals include building a dedicated new training centre bringing facilities for the first team, development squad and youth team players under one roof.
The build will also include an indoor all-weather area with a small spectator gallery, to meet the requirements of the Elite Player Performance Plan (EPPP).
Three full-sized training pitches, each measuring 68m x 105m will be developed, while a further two three-quarter size pitches will be added for youth team players.
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The plans were approved by the council's Planning Committee.
However, the proposed site falls within the green belt, meaning the Government's Secretary of State could still 'call in' the plans for further consideration.
Club Director Clive Holt said: "We have been trying to reach this day over a number of years to bring our facilities up to the latest standard.
"This has been greatly helped by last season in the Premier League and the rewards that brings.
"We now look forward to entering a new era for Burnley Football Club and taking this club forward for generations to come."
Operations Manager Doug Metcalfe added: "The process to get to this point has been long and arduous, but we are delighted that a positive outcome has been achieved for the club.
"We have never lost focus on the importance of these facilities and the hugely positive effect it will undoubtedly have in the development of the club and its vision.
"Although we have carried out some redevelopment work to our existing facility in recent years, they were still a long way short of what we require.
"The new environment will allow us to provide the facilities necessary to continually develop the club."
(LM)
