Royal Barnes is also accused of “glorifying” an act of terrorism by publishing a statement entitled “Muslim laughs at British Soldier killing”.
He faces a third charge of inciting terrorism overseas.
He appeared at Westminster Magistrates' Court and is due to appear at the Old Bailey on Friday.
Mr Barnes, from east London, was detained by police on Friday along with a 21-year-old woman who is due to answer bail on Tuesday.
Two men – Michael Adebolajo, 28, and Michael Adebowale, 22 – have been charged with Fusilier Rigby's murder on 22 May.
Scotland Yard said Mr Barnes had been charged with dissemination of terrorist publications for allegedly making a series of recordings about the killing on the day it took place, and circulating them “with the intention, either directly or indirectly, of encouraging others into the commission, preparation or instigation of an act of terrorism”.
He is also accused of encouraging an act of terrorism by publishing a statement that glorified the killing.
On the final charge, it is claimed that on 12 June he “incited another to commit an act of terrorism, wholly or partly outside the United Kingdom, and that act, would if committed in England and Wales constitute an offence”.