Jonathan Chew, 24, of no fixed address, was charged on Monday with common assault and obstructing police and will appear at Westminster Magistrates’ Court on Tuesday, the Metropolitan Police said.
England’s chief medical officer was accosted by two men on 27 June as he walked through St James’ Park in central London.
Videos posted online showed the pair grabbing and shoving Prof Whitty, heard shouting “oi oi” and “one photo please” as he tries to break free.
Following swift condemnation of the incident by politicians across Westminster, the police launched an investigation.
Prof Whitty, who did not suffer any injuries, was spoken to by officers, who also reviewed the 20-second video posted on social media.
Last week, another man was arrested and charged with common assault: Lewis Hughes, 23, of Wigton Way, Romford, east London.
He is due to appear at Westminster Magistrates’ Court on Friday July 30.
Mr Hughes, a 24-year-old estate agent who had attended an anti-vax march earlier that day, said he had lost his job following the incident, telling The Sun: “I absolutely apologise for any upset I caused.”
He added: “If I made him feel uncomfortable, which it does look like I did, then I am sorry to him for that.
“He is quite a timid, shy person and I think that is why he didn’t say, ‘Get off me’. If he had said that and I had realised how he felt, I wouldn’t have put my arm round him.”
He said he had been hoping to get a selfie with Prof Whitty to show to his mother, adding: “There was no malicious intent, I didn’t want to upset him.”
Earlier, Boris Johnson had described Prof Whitty’s assailants as “thugs”.
“I’m shocked at seeing the despicable harassment of chief medical officer Chris Whitty,” Mr Johnson said.
“I condemn the behaviour of these thugs. Our hard-working public servants should not have to face this kind of intimidation on our streets and we will not tolerate it.”