Police are appealing for information after the men, believed to be in their 60s, were hit in Western Road, Romford.
They died at the scene.
The driver of the 252 double decker bus has been arrested on suspicion of causing death by dangerous driving.
He is currently in custody at an unnamed east London police station.
London Ambulance Service paramedics were called to Western Road at 2.20pm.
Two single responders, a duty officer and an ambulance crew were sent to the scene of the accident, at the road’s junction with Chandlers Way.
The 252 travels from Collier Row Library to Hornchurch town centre.
Eyewitness Patrica Kluxem, 49, of Collier Row, who was on the bus at the time, said: “There were two bangs and a big cry. I was in so much shock, everybody got off the bus and there was lots of shopping on the floor.
“I was crying, I called my pastor after to tell him what happened.”
It is believed the Liberty Shopping Centre closed its doors after the collision.
Another passenger said he heard a “bang” and felt a “thud”, adding: “everybody started panicking, saying ‘someone has been hurt.’”
Police believe there were a large number of witnesses at the scene, including those on the bus involved and another one that was passing at the time of the incident – understood to have been a 103.
Detectives want those people to come forward with any information they may have.