Spartak Moscow, the only Russian club left in the competition, have been drawn against RB Leipzig. Spartak will be unable to play their home game in their country and will have to find a neutral venue, a decision taken by UEFA's Executive Committee on Friday following Russia's military invasion of Ukraine.
Barca, who have never won the competition, are looking to become the third consecutive Spanish side to lift the title after Sevilla and Villarreal.
Barca failed to make it past the Champions League group stages for the first time in 22 years and are taking part in their first Europa League competition since 2004. Xavi Hernandez's side reached the round of 16 after a convincing 4-2 win (5-3 on agg.) at Napoli on Thursday. Barca will play the opener at home and then travel to Turkey for the return leg.
Record six-time Europa League winners Sevilla will take on West Ham, a team they have never faced that is sixth in the Premier League.
They have an added motivation to go all the way in the competition with the final being staged on May 18 at their Ramon Sanchez Pizjuan stadium.
Despite Thursday's 1-0 defeat at Dinamo Zagreb, Sevilla progressed 3-2 on aggregate.
"We were drawn with perhaps the most difficult [rival] of all," Sevilla's sporting director Monchi said. "A very well-built team, that is having a great season in the Premier League. They have players of a high level, both technical and physical.
"We haven't been very lucky, but we must assume that draws are like that and look forward with optimism. I don't think they will be too happy either.
"It's a good tie, worthy of the importance of the competition. it will be a beautiful experience, it [England] is the cradle of the game of football and this tie will allow us to measure our ability to overcome challenges."
The other Spanish side left in the competition, Real Betis, square off against Eintracht Frankfurt. Betis knocked Sevilla out of the Copa del Rey last month. They eliminated Russian Premier League champions Zenit 3-2 on aggregate.
Scottish champions Glasgow Rangers, who saw off Borussia Dortmund and their Norwegian superstar Erling Haaland on Thursday, are back in the round of 16 for a third straight season. They take on Red Star Belgrade.
Meanwhile, in the Europa Conference League, Leicester City have been drawn against Stade Rennais. The Premier League side reached the round of 16 after eliminating Danish side Randers 7-2 on aggregate.
The round of 16 first legs will be played on March 10, except for FC Porto and Betis who will play at home a day earlier, while the returns will be taking place on March 17.
Europa League round of 16
Rangers vs. Red Star Belgrade
Braga vs. AS Monaco
FC Porto vs. Lyon
Atalanta vs. Bayer Leverkusen
Sevilla vs. West Ham United
Barcelona vs. Galatasaray
RB Leipzig vs. Spartak Moscow
Real Betis vs. Eintracht Frankfurt
Europa Conference League round of 16
Leicester City vs. Stade Rennais
Marseille vs. FC Basel
PAOK Salonika vs. KAA Gent
Vitesse vs. AS Roma
PSV Eindhoven vs. Copenhagen
Slavia Praha vs. LASK
Bodo/Glimt vs. AZ Alkmaar
Partizan Belgrade vs. Feyenoord Rotterdam