The 41-year-old was arrested Thursday morning on suspicion of causing grievous bodily harm after officers searched an address in the affluent Chelsea area of the city.
Police have not named the person they arrested, but lawyers for a man named Eric Bellquist came forward on Friday to say his client had "irrefutable proof" that he was in the United States at the time.
"Our client has been wrongly implicated in this matter; he categorically denies being the individual concerned and has irrefutable proof that he was in the United States at the time of the incident," Duncan Lewis Solicitors said in a statement.
CCTV footage of the incident, which happened on May 5 but was released this week, appears to show a male jogger knocking a 33-year-old woman into the road as she walked across Putney Bridge in west London.
Seconds later, a bus is seen swerving out of the way, and narrowly missing the woman, who suffered minor injuries.
Metropolitan Police say the jogger came back across the bridge 15 minutes later; the victim tried to speak to him but he did not acknowledge her and carried on jogging.
In a statement, police said the man they arrested had been cleared "with no further action" to be taken. He had already been freed from police custody but had remained under investigation until Saturday.
Officers investigating the attack have renewed their appeal for information on the jogger, who they describe as a white man,