Welbeck, sidelined since last April with knee injuries, made his comeback against Leicester City on Sunday, grabbing an injury-time winner against the league leaders to keep Arsenal firmly in the title race.
Arsenal are third in the Premier League behind Tottenham Hotspur on goal difference and face potentially decisive fixtures over the next few weeks.
They take on Championship (second-tier) side Hull City in the FA Cup on Saturday followed by the first leg of their Champions League last-16 tie against Barcelona in midweek and a Premier League trip to Manchester United the weekend after.
"For Danny to go through a bad, injured period where he kept believing in himself, when everyone maybe doubted him, it was a great chance for him to come in and show he was ready to give everything for the team," Mertesacker told the club's website.
"We have long-term injuries, which gave us a bit of a struggle, especially in January, where we played in December and January with almost the same team.
"We are happy to have Danny now and a few others are not far away. We need our players - you could see that makes a difference."