The plans had been submitted to Reading Borough Council earlier in the year and were approved at a planning meeting on Wednesday night.
Chief executive Nigel Howe told readingfc.co.uk: "This is great news and is very exciting for both the football club, our fans and the region as a whole. The expansion will allow us to take the club forward and further improve the facilities for our supporters as we aim to become an established force in the top flight."
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