The on-field umpires called off the match after an inspection at 11.30 local time.
It is the first time in the history of Test cricket in India that four days have been completely washed out.
The last time a major part of a Test in India was washed out was almost a decade ago when play was held up for three days in a Test in Chennai between India and Sri Lanka.
Though it only drizzled briefly on the fifth and final morning, overnight rain meant there could be no play.
Puddles had formed in a few uncovered areas near the edges of the ground at the Chinnaswami Stadium.
It is likely the umpires felt that patches of damp spots in some of the areas, caused by sweating under the covers, might not be safe for fielders.
Besides the super soppers, the groundstaffs also had in their disposal a machine called the Pro Core, but none could ensure resumption of play in South African batting mainstay A B de Villiers;' 100th Test.
India skipper Virat Kohli said after the match, "The bowlers did a commendable job, bowling South Africa out in less than three sessions is something that's very rare. A lot of people were surprised when we decided to field first. All credit to the bowlers, Bangalore is known for its runs, but our bowlers showed their character.
"It's a pity that we lost four days when we were in such a strong position.
Rival captain Hashim Amla said, "We've had about seven days of Tests in 20 in the last four Test matches. Very surprised we have lost four days of cricket here. I really didn't think four days would be washed out.
The bowling looked ordinary with the pacers struggling to get the ball in the block hole but Kohli had said in the post-match presentation about the pitch being a batting beauty.
Ravichandran Ashwin didnt have a great match but the champion bowler that he is, Kohli and coach Anil Kumble knows that he will be back anytime. They have a back-up spinner in Amit Mishra.
England would need something extraordinary to recover from the body blows as they have to win the remaining two matches which would requite quite a feat.
Back to lead the side after pulling out from the Bangladesh series, English limited overs skipper Morgan will be under pressure to transform their bowling unit which performed abysmally in Pune.
No doubt, Ben Stokes did well with the bat wtih his 40-ball 62 to take them to their best ever but his effort with the ball (2/73) was found wanting as they struggled to take a wicket for 25 overs when Kohli-Jadhav engineered the win.
The English bowling is still struggling to find a way to stop Kohli, something that will hurt the visitors who were swept 0-4 in the five-match Test series and now their hope to recover in the limited overs is too going away fast.
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