The home side, who resumed on 97-0, needed just 5.3 more overs to reach a victory target of 130.
England thrashed South Africa by nine wickets in the third and deciding Test at the Oval on Monday, completing a 2-1 series win in just over two days of action.
The home side, who resumed on 97-0, needed just 5.3 more overs to reach a victory target of 130. Zak Crawley was 69 not out and Ollie Pope 11 not out.
England have now won six of their seven Tests under their new leadership pairing of captain Ben Stokes and coach Brendon McCullum, having managed just one victory in their previous 17 matches when former skipper Joe Root was in charge.
Defeat means South Africa have suffered their first Test series loss since Dean Elgar took over as captain last year.
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