The decision on Wednesday afternoon by the Division I Board of Directors, which oversees the most prominent tier of college athletics in the United States, amounted to a surrender to years of swelling legal and political pressure. The board acted less than 12 hours before state laws designed to challenge the N.C.A.A.’s generations-old rules were scheduled to begin taking effect from Alabama to Oregon. Leaders in Divisions II and III, which include less visible and wealthy athletic programs but hundreds of thousands of players, made similar moves. The N.C.A.A.’s last-minute policy change, which players and executives alike view as one of the most significant changes in the association’s 115-year history, will allow athletes to make endorsement deals whether or not they attend college in a state with one of the laws that forced the industry to act.