Final answer:
William Shakespeare was part of The King's Men from 1603 until his death in 1616, making it approximately 13 years. He was an actor, playwright, and part owner of the troupe, contributing to their works until the very end of his life.
Step-by-step explanation:
William Shakespeare was a crucial member of The King's Men for approximately 13 years. Beginning in 1603, when King James I took the throne and sponsored the company, the troupe formerly known as The Lord Chamberlain's Men was then renamed to The King's Men. Shakespeare's involvement with the theater troupe as an actor, playwright, and part owner spanned over two decades in total.
Among the last works he contributed to before his death in 1616 was 'The Two Noble Kinsmen,' penned with John Fletcher around 1613. His career with the King's Men represents the latter part of his overall work within the London theater scene.