George knew Lennie's aunt, who used to care for Lennie. When she dies, George promises to look after and take care of Lennie.
George and Lennie met as a result of George originally meeting and getting to know Lennie's Aunt Clara. She was the woman who devoted a part of her life to rearing Lennie. Upon her death, George Milton became the guardian of Lennie, as his protector, as Lennie is of limited mental acuity.
Lennie’s full name in this novel by writer John Steinbeck is Lennie Small, the last name a literary device that is indicative of how the world sees Lennie as concerns his mental ability, but not how they see him physically, as he is of great strength.
George, through knowing Lennie’s Aunt Clara, came to know Lennie and agreed to take on the responsibility of caring for Lennie upon her death. Lennie and George have been friends since childhood. Later in life, this leads to George and Lennie traversing California in search of better job (and overall life) prospects. They dream of living peacefully and working off the land together – a quiet, humble life that is not to be for Lennie, and ultimately, maybe not even George when all is said and done in his life.
They met because George had an acquittance with Lennie's aunt Clara and when she died she wanted George to take care of Lennie because of him being handicapped.