The Yorkshireman, 66, won 14 England caps between 1969 and 1971, leading his country on four occasions, and toured New Zealand with the 1971 Lions.
He said: "It is a privilege and honour to represent the Lions as tour manager, 46 years after I did so as a player."
Spencer succeeds Scot Andy Irvine, who oversaw the 2013 triumph in Australia.
He is the third English Lions tour manager in rugby union's professional era, following Fran Cotton (South Africa 1997) and Bill Beaumont (New Zealand 2005).
Former Ireland captain Tom Grace, who toured with the Lions to South Africa in 1974 and is currently treasurer of the Irish Rugby Union, will succeed Welshman Gerald Davies as chairman of the British and Irish Lions board.