"When I had the world record at 8.29m, I thought that it might be difficult to beat it, but then to go on and get 8.40m was really special," said Rehm after his gold medal-winning performance.
"I woke up feeling that it was going to be my day. Thankfully it all worked out for me."
Earlier this week, Rehm said he wanted to get close to Rutherford's winning distance in China.
"Of course I am looking to the world championships. Of course it's different conditions and everything is different, but, yeah, I compare myself to other athletes," he said.
"I look at the world rankings, at how far they can go and how far I go, and that is definitely what I am looking for."
The IAAF are expected to rule soon on whether Rehm can compete at the Rio Olympics. If he does compete, Rehm should be a medal contender.
In 2014 he recorded the best jump, 8.24m, at the German trials for the European championships. His leap yesterday was the sixth best long jump recorded this year.
His jump would also have been long enough to have secured gold at the last Olympics, in London 2012.
- AAP