The incident happened in Forbes Road at about 10:25. The van driver had picked up the thief in Yeaman Place in his red Renault Trafic van.
As he dropped him off in Forbes Road, the thief pulled out a knife.
He took a two-figure sum of money and left in the direction of Bruntsfield Place.
He was about 30 years old, white, about 6ft tall and of medium build. He was wearing a dark jacket with a white stripe on the sleeve and dark jeans.
Police have appealed for witnesses.
Det Con Joyce Gunderson said: "Thankfully the van driver was not injured during this robbery but he was left understandably shaken.
"We are pursuing various lines of inquiry to trace the man responsible and we are keen to hear from anyone who can assist us in identifying him.
A thief who stole money at knifepoint from a van driver he had just caught a lift from in Edinburgh is being sought by police.