The 30-year-old, who has eight England caps, established himself as one of his country's top keepers during 141 league appearances for the Clarets.
Mikel Arteta castigated his Arsenal side for throwing away a season's work in a limp 2-0 defeat at Newcastle.
A look at what’s happening in European football on February 13
United fell to fifth place, a point behind West Ham, which was a 1-0 winner over Watford on Tuesday.
Newcastle United have signed Ashington-born defender Dan Burn from Brighton & Hove Albion for an undisclosed fee.
While the victory meant Liverpool stayed on the shoulder of league leader Manchester City in what is shaping up to be an exciting title race, Chelsea couldn't keep pace.
A freeze on any clubs signing commercial deals with companies linked to their ownership was rushed through temporarily last month after the Saudi sovereign wealth fund bought Newcastle.
The former Bournemouth boss succeeds Steve Bruce, who left the Premier League club by "mutual consent" on October 20.
Emery said he was grateful for being considered for the Newcastle job but was “even more grateful” for being able to continue with the Spanish club.
Manchester City are now five points off the top after Pep Guardiola's 10 men were beaten 2-0 by Crystal Palace at the Etihad.
In an official release, Steve Bruce said: "I am grateful to everyone connected with Newcastle United for the opportunity to manage this unique football club."
AS Roma is currently at the fourth position in Serie A standings with 15 points from seven games.
Many activists have alleged that the MBS and Saudi Arabia are using this to cleanse their reputation globally and to shift the discussion from the lack of democracy in the country.
Hatice Cengiz said the £300 million ($408 million) takeover deal was "heartbreaking" for her and she was "very disappointed".
Brazilian midfielder Raphinha gave Leeds a 13th-minute lead when his cross was cleverly dummied by Rodrigo as it curled past Newcastle goalkeeper Karl Darlow.