The OM founder was addressing thousands of European Christians on the final night of the Mission-Net Congress in Erfurt, Germany.
"If people like you don't go, who will?" he said, dressed in his trademark 'world map' jacket.
In an impassioned plea with the participants, Verwer said he was praying to God every day for workers to go out to the world's "forgotten places".
"The word of God is clear," he said. "Don't be hearers of the word, be doers."
Verwer spoke openly about his own personal struggles with lust and sexual sin, as he reassured the audience that God loved them and wanted to use them in spite of any moral failings or mistakes.
"It's easier to talk sometimes about the greatness of God than about ourselves … but when we look at the Bible we see: God uses people."
Verwer said he honoured Christians who choose to follow a profession in a field such as medicine or law, but added that the estimated two billion unreached people of the world would never be reached without Christians who dedicate themselves to mission full-time.
Those unable to do so need, he said, to get hold of a copy of "Operation World" and start praying regularly for the nations, for leaders and for churches planted in the largely unevangelised countries.
"We need Christians in every area of society but if we are serious about global missions, we need to include mission work as a legitimate career for this generation," he said.
"I appeal to you to go into short-term missions this year or in the next two years, or at least start moving in faith towards long-term mission work."
Around 2,500 young Christians from 40 nations in Europe attended the weeklong Congress in Erfurt, the city where Martin Luther spent 10 years.
Mission Net is held every two years and is an initiative of the European Evangelical Mission Association and the European Evangelical Alliance.