The crowd in St Peter's Square chanted "Long live the Pope", waved banners and broke into sustained applause as he spoke from his window.
The 85-year-old, who will resign on February 28, thanked the crowd in several languages.
The Vatican estimated the crowd at more than 50,000 people, larger than the size which turns out at a normal Sunday address not linked to a specific liturgical feast.
Speaking in Spanish, the Pope said: "I beg you to continue praying for me and for the next Pope." It was not clear why the Pope chose Spanish to make the only specific reference to his upcoming resignation.
However, a number of cardinals have said they would be open to the possibility of a Pope from the developing world, be it Latin America, Africa or Asia.
After his address, the Pope retired into the Vatican for a scheduled, week-long spiritual retreat and will not make any public appearances until next Sunday.
Speaking in Italian in an earlier part of his address about the season of Lent, in which Christians reflect on their failings and seek guidance in prayer, the Pope spoke of the difficulty of making important decisions.
He said: "In decisive moments of life, or, on closer inspection, at every moment in life, we are at a crossroads: do we want to follow the 'I' or God? The individual interest or the real good, that which is really good?"
Since his announcement last week, the Pope has said several times that he made his decision to become the first Pope in more than six centuries to resign "for the good of the Church".
The Pope says his physical and spiritual forces are no longer strong enough to sustain him in the job of leading the world's some 1.2 billion Roman Catholics at a time of difficulties for the Church in a fast-changing world.