The former England Under-21 international has progressed through the youth system at Goodison Park and made nine appearances for the Toffees.
Browning, 22, missed the end of last season with a knee injury that kept him out for nearly a year.
"I hope to be able to come in and make an impact," he told the club website.
"I have heard nothing but good things about the club and can't wait to get started."
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Internet service providers had until Tuesday to implement the ban.
The sites now redirect to a message explaining they have been blocked "by decision of public authorities".
In 2015, the authorities banned 11 popular pornography websites, saying many failed to protect children "from information harmful to their health".
Analysis by Vitaliy Shevchenko, BBC Monitoring
The decision was made following two separate court rulings, which said the websites "spread pornography".
Sexually explicit content is not outlawed in Russia, but the law bans "the illegal production, dissemination and advertisement of pornographic materials and objects".
It is not uncommon for Russia to ban websites. The government agency Roskomnadzor maintains a blacklist that now includes thousands of them.
Access is usually blocked for violating the notoriously vague extremism legislation or child protection laws.
Websites critical of the Kremlin have been blocked too, and at one point Wikipedia was blacklisted.
Following the 2015 ban, one woman asked Roskomnadzor on Twitter whether it could recommend an alternative.
The agency replied: "You can meet someone in real life."
On Tuesday, it said its earlier tweet was "still relevant".
However, open rights campaigners have warned that local bans can be defeated.
"Blocking porn is the fastest way to ensure widespread adoption of censorship circumvention in your country," said Eva Galperin, global policy analyst at the Electronic Frontier Foundation.
One of the affected porn sites offered Roskomnadzor a premium subscription to its service, in exchange for lifting the ban.
The government agency said it was "not in the market" for such an offer.
Nadya Tolokonnikova, lead singer from punk band Pussy Riot, joked that the ban was "a blow below the belt".

The Scottish FA says the paperwork for the player who joined Celtic from Ashdod in 2012 was completed in time before the 23:00 GMT deadline.
But their English counterparts have different rules regarding work permits.
And the 28-year-old, who has played 51 times for his country, does not automatically meet the FA's criteria.
Because Nigeria are ranked 50th in the world, he would require to have played at least 75% of their country's matches over the previous two years.
Ambrose played twice last year and three times in the previous 12 months.
The defender has fallen out of favour at Celtic this season since Brendan Rodgers took over as manager.
He has only made two appearances, the last being a Champions League qualifier against Astana in July.
Should he join Blackburn, he could partner former Celtic team-mate Charlie Mulgrew, who made the switch last summer, in the Championship side's central defence.
However, he has also played at right-back and for Nigeria in central midfield.
His move came on a day when Chelsea failed in a bid to sign Celtic goalkeeper Craig Gordon, while nothing came of reports of interest from the English Premier League leaders in his team-mate, striker Moussa Dembele.
The only other movement out of Celtic on deadline day was goalkeeper Leo Fasan and defender Jamie McCart joining Port Vale and Inverness Caledonian Thistle respectively on loan and winger Michael Duffy leaving on a permanent transfer to Irish club Dundalk.
Everton defender Tyias Browning has signed a new two-and-a-half-year deal and joined Championship side Preston on loan for the rest of the season.
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Russia's media watchdog, Roskomnadzor, has blocked access to two of the world's largest pornography websites.
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Efe Ambrose's proposed loan move from Celtic to Blackburn Rovers is awaiting an English FA ruling over a work permit for the Nigeria defender.