Scotland Yard identified the men as an 18-year-old and a 32-year-old, but didn't give their names. The force said in a statement the pair was arrested early Thursday at separate addresses in east London.
A man who identified himself as a friend of the detainees identified the 18-year-old as Jamal ud-Din and said the older man was someone he knew only as "Zakariya."
Mizanur Rahman, 29, said the arrests "might have had something to do with the fact that they recently went canoeing" on the River Lee, a branch of which runs through the Olympic site in east London. He said the pair also recently went shooting with an air rifle in Essex, a largely suburban and rural county east of London.
Rahman said he saw nothing amiss with the activities. "It's just people trying to get into the Olympic spirit," he said, adding that he believed authorities would try "painting it as jihad training."
Rahman pointed the AP to what he said was a photograph of ud-Din. The picture showed a stocky, pale-faced man with a bushy red beard and it appeared to match a man who appeared last year in a YouTube video entitled "The Test of Allah by Jamal ud Deen."
The speaker on the video, who Rahman confirmed was ud-Din, expresses contempt for democracy and non-Muslims, admiration for Islamist firebrands including jailed Egyptian preacher Abu Hamza, and anger at the Danish cartoons which infamously caricatured Muhammad whom Muslims revere as a prophet.
At one point the speaker approvingly quotes someone he refers to only as "the sheikh."
"We're not like the Christians; if you slap us on the left cheek, we'll slap you back," he tells an unseen audience. "This is so true, brother. We're Muslims. We defend ourselves, brother."
Security services across Europe have long been alert to the activities of extremist Muslim converts.
Richard Reid, who tried to blow up a trans-Atlantic flight in 2001, was a convert. So, too, was Jermaine Lindsay, one of four suicide bombers in London's 2005 attacks. The coordinated bombings killed 52 people just one day after London won the bid for the Olympics. In 2010, two German converts to Islam and two Turkish men were convicted over a foiled plot to attack U.S. targets in Germany.
This week European security officials told the AP that they were tracking a Norwegian Muslim convert who had gone to Yemen for training and had since become "operational."
Intelligence officials say there has been an expected increase in chatter among extremist groups, but there are still no specific or credible threats targeting the Olympics. The terror level is labeled substantial, a notch below severe.
A substantial threat level indicates that an attack is a strong possibility.