Dubbed "The Finale", the four shows will see her play to more than 300,000 fans as she wraps up her world tour.
The new shows will be on 28 June and 2 July, 2017, with tickets on sale from 7 December to members of her fan club.
Take That hold the record for playing the most dates at Wembley, having staged eight nights of their Progress tour there in 2011.
The previous record holder was Michael Jackson, who brought his Bad tour to the stadium five times in 1988.
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Pop star Adele has added two further dates at Wembley Stadium next year, after the initial concerts sold out.