The man was arrested on suspicion of preparing for terrorist acts and terrorist training as he stepped off the plane from Istanbul on Thursday evening.
He remains in custody at a south London police station.
Officers are searching a property in east London, Scotland Yard said.

Sales volumes increased by 1.7% in November from the month before, the Office for National Statistics said.
Compared with the same month last year, sales were up by 5%.
However, Keith Richardson from Lloyds Bank Commercial Banking said it was "too early" to say whether Black Friday was really a success for retailers.
"Retailers were better prepared this year and adapted the US-style Black Friday to better reflect British culture. Some chose not to take part while many others spread the discounts over several days to better protect margins and ease the burden on their websites and IT platforms."
The ONS said the amount spent by shoppers was up 1.4% in November compared with the month before, and was also up 1.4% from the same point a year earlier.
The value of online sales increased by 4.9% in November from October, and were 12.7% higher compared with last year.
"Retailers may see some pay-back after the Black Friday promotions led shoppers to pull-forward spending that would otherwise have taken place in December, but the underlying sales trend looks set to remain strong as we head into 2016," said Chris Williamson, chief economist at Markit.
He added that spending was not just being driven by discounts. "Households are benefitting from improved job security, low inflation and falling energy prices, the latter helping free-up more income to boost retail sales."

The cost of borrowing will remain unchanged at 6.25% ahead of a possible increase in US interest rates later this month.
The decision came as the Reserve Bank of India (RBI) held its first press conference since new bank notes were introduced.
The BBC was one of several media organisations prevented from attending the briefing.
The central bank blamed a decision to move the press conference to a small venue.
The Reserve Bank of India gave no clear reason for its unprecedented decision to exclude some media organisations including the BBC from attending today's press conference held by its governor, Urjit Patel, after the monetary policy meeting.
"Space constraint" is the only official response we were given. That is somewhat ironic considering that only last year the RBI started holding press conferences in a bigger room to accommodate more journalists.
The tradition has been that the Governor of the Reserve Bank of India addresses a long press conference after the monetary policy decision. And it's open to all media organisations. I have attended many such events in the past.
We have been told that the decision to exclude certain media organisations had nothing to do with the coverage of the recent currency note ban in India - which received widespread criticism for its implementation.
There are concerns that the cash clampdown could cut growth in the world's fastest-growing major economy.
Expectations of a rate cut rose last week after India reported lower-than-expected economic growth of 7.3% for the three months to September.
That put pressure on the central bank, particularly after Prime Minister Narendra Modi said on 8 November that 500 ($7.30; Â£6) and 1,000 rupee notes would no longer be legal tender.
While demonetisation was a government decision, it had to be approved by the Reserve Bank. This has led to strong criticism of Mr Patel and the transparency of his institution.
The governor reduced the cost of borrowing when he took up the post in October and replaced Raghuram Rajan, who chose to leave the RBI without seeking a second term.
It was the third cut in rates this year after reductions in January and March.
Mr Patel is known to take a tough line on inflation, which remains one of the big worries in the Indian economy.
But fresh worries have emerged after the government's decision to ban 500 and 1,000 rupee bank notes, which caused chaos as people lined up at banks to exchange their old currency.
Some banks ran out of cash. At others, police were called in to manage queues of anxious customers hoping to change their savings for legal tender.
The surprise government move is aimed at tackling corruption and tax evasion.
But many low-income Indians, traders and ordinary savers who rely on the cash economy have been badly hit. The two notes accounted for about 86% of the cash in circulation.
A 30-year-old man arriving in the UK on a flight from Turkey has been arrested at Heathrow Airport by counter-terror police.
[NEXT_CONCEPT]
UK retail sales rose by more than expected in November, as shops offered promotions at the end of the month in the run up to Black Friday.
[NEXT_CONCEPT]
India's central bank has unexpectedly held interest rates at a six-year low.