The Metropolitan Police said in a statement that the men were arrested by its Counter Terrorism Command on November 28.
Rahman, from Finchley in north London, is charged with preparing acts of terrorism and assisting Imran in terror planning.
Sky News quoted its correspondent as saying there was an "extreme Islamist suicide plot against Downing Street (a reference to the UK Prime Minister's residence)".
A 20-year-old man accused of a plot to bomb Downing Street's security gates and then kill British Prime Minister Theresa May was on Wednesday remanded in custody after he appeared at a court here.
Details of the assassination plot were reportedly given to the Cabinet on Tuesday by head of MI5 Andrew Parker in a briefing in which he revealed that a total of nine Islamist terrorist plots have been thwarted in the United Kingdom over the past year.
Also accused is 21-year-old Mohammed Aqib Imran, who was arrested in Birmingham.
The two accused men were arrested last week HandcuffsFlickr
This year in the United Kingdom there have been five terrorist attacks.
"The secondary attack was to be carried out with a suicide vest, pepper spray and a knife", he told the court. When asked about his nationality in court, Imran said he was Bangladeshi British.
Imran was accused of trying to join Daesh in Libya, the prosecutor alleged. An official report into the attack released on Tuesday found opportunities to thwart it had been missed.
Downing Street was targeted by the Irish Republican Army (IRA) in 1991 when a mortar bomb attack was launched.
"Cabinet ministers heard that while IS suffered major defeats in Iraq and Syria, this did not mean the threat is over".
Britain has seen five terror attacks this year, which killed 36 people and injured more than 200 others.