The England Under-19 international, who has not played a Premier League game for the Gunners, will move to the Estadio da Luz on a five-year deal.
Willock, 19, had been offered a new deal at Arsenal, but his move to Lisbon has been revealed via Benfica's Twitter feed.
Manchester City had also been linked with the attacker, whose contract expires on 1 July.
"I hope I can show what I can do on the pitch. I think we have a great team and we can achieve great things in the future," Willock said on the Benfica website.
Willock had been with Arsenal since 2003 with his younger brother, Joe, remaining in the Gunners youth set-up.
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Highways England has said its preferred route for a new Lower Thames Crossing is a tunnel connecting Gravesend, in Kent, to Tilbury, Essex.
However, Tory MP for Gravesham, Adam Holloway, said the government should instead build a new tunnel between Dartford and Thurrock.
He claimed there would be "carnage" if the M25 at Dartford was "not fixed".
"This is quite simply the worst stretch of road in the UK, and it has a huge impact on local residents," Mr Holloway told MPs during a parliamentary debate on Monday.
"There are entirely viable schemes, including a seven-mile tunnel under Dartford and Thurrock," he said.
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The Conservative MP for Dartford, Gareth Johnson, suggested Mr Holloway was in favour of "funnelling more traffic" towards the existing Dartford Crossing and in to the Dartford area.
He said: "Isn't it the situation that we should have more resilience, as we have across the rest of the Thames, so you have crossings at various different locations?
"The solution surely is to take traffic away and put the crossing east of Gravesend."
But Mr Holloway said the "Â£5bn opportunity to fix the M25 is about to be wasted," adding that it will soon be "too late to stop a plan that's going to result in another 30 years of misery on the M25".
He added: "Have a conversation about something to the east of Gravesend, or wherever it is, but let's not confuse two things.
"The problem is a disaster at Dartford and it is going to be a complete scandal."
Concluding the debate, transport minister John Hayes said more than 47,000 people had taken part in a consultation on the preferred option for the crossing and the government was currently analysing the results.

The event was missing from calendar in 2014 and 2015 because of financial limitations but is set to return as the first race of the season next year.
The organising club have applied for Friday 1 April and Saturday 2 April as its dates for next year.
A new title sponsor, JFM Haulage, has been acquired for the event.
Traditionally, the Cookstown 100 has been the first race of the Irish road racing season, but that is set to change next year.
The April date switch has still to be ratified by the sport's governing body, the MCUI, Ulster Centre, however.
The race will still be held over the 3.6-mile Clough course, although work will be carried out to certain parts of the course.
For many years, the Mid Antrim was staged in August, although a June date was experimented with in 2012, before the event reverted back to its usual August date the following season.

A window of a property on Aubrey Street was smashed when a group of people threw a bin at it at about 1:45 GMT on Sunday.
The five adults inside the house were not injured.
Police have asked for anyone with information on the attack to contact them on the non-emergency number 101.
Arsenal forward Chris Willock is to join Benfica when his contract expires.
[NEXT_CONCEPT]
A proposed new road tunnel beneath the River Thames would lead to 30 years of "misery" on the M25, an MP has warned.
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The organisers of the Mid Antrim 150 have applied for an early April date as they seek to resurrect the national road race in 2016.
[NEXT_CONCEPT]
An attack on a house in Londonderry is being treated as a sectarian hate crime, police have said.