The pair only broke into Sean Dyche's side on a regular basis this season but have been instrumental in the Lancashire club's rise to seventh place in the Premier League table.
Swansea defender Alfie Mawson was also given his maiden call-up while uncapped Bournemouth midfielder Lewis Cook, who was named in the squad for November's friendly against Brazil but did not play, was included again.
Goalkeeper Joe Hart remained in the squad despite a difficult season for West Ham United where he has been left out of the side for several games.
Another surprising inclusion was Arsenal forward Danny Welbeck who has not been a regular starter for Arsene Wenger's side in their difficult campaign.
But there was no place for Chelsea defender Gary Cahill who has recently been left out of his club side.
Southgate said he was pleased Wilshere was fit again and appearing regularly for Arsenal.
"Jack's a player that has unquestionable talent. The key for me is that he is playing in the games that matter for Arsenal. He's getting closer to where we want him," he said.
"His technical ability in the middle of the park will be very useful," added Southgate, who said he was keen to look at new players.
The England manager said that although Cahill remained in contention for a World Cup spot if he can regain his place at Chelsea, he felt it was prudent to assess Tarkowski and Mawson.
"Tarkowski and Mawson are players you want to look at for now and beyond the summer. I want to see (Eric) Dier in a back three too," he said.
"It was a very difficult call because Cahill has played a lot of qualifiers and is a great guy."
Southgate said Pope's form merited a call-up to a competitive goalkeeping group.
"Clearly the number one jersey is up for grabs," said Southgate. "From our point of view he (Hart) he has been our number one through qualifying, he is an important member of the squad so we wanted to keep him involved."
Tottenham Hotspur striker Harry Kane is missing the two games due to an ankle injury.
Southgate's side will play the Netherlands on March 23 in Amsterdam before hosting Italy at Wembley Stadium on March 27.
England squad:
Goalkeepers: Joe Hart (West Ham United), Jack Butland (Stoke), Jordan Pickford (Everton), Nick Pope (Burnley).
Defenders: Joe Gomez (Liverpool), Kieran Trippier (Tottenham), Kyle Walker (Man City), John Stones (Manchester City), James Tarkowski (Burnley), Alfie Mawson (Swansea), Harry Maguire (Leicester City), Ashley Young (Manchester United), Danny Rose (Tottenham).
Midfielders: Dele Alli (Tottenham), Lewis Cook (Bournemouth), Eric Dier (Tottenham), Jordan Henderson (Liverpool), Adam Lallana (Liverpool), Jesse Lingard (Manchester United), Jake Livermore (West Brom), Alex Oxlade-Chamberlain (Liverpool), Jack Wilshere (Arsenal).
Forwards: Marcus Rashford (Manchester United), Raheem Sterling (Manchester City), Jamie Vardy (Leicester City), Danny Welbeck (Arsenal)
(Reporting by Simon Evans, editing by Pritha Sarkar and Ed Osmond)
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