Sprint Corp. has proposed a merger with Charter Communications Inc. that would create a media and communications giant, upending industries that are already in the throes of dramatic change.

Since the end of May, Charter and Comcast Corp. had been in exclusive talks with Sprint over possible deals, including one that would allow the cable companies to resell wireless service under their own brands. Though the exclusivity window ended this week, Sprint Chairman Masayoshi Son continues to pursue a much larger deal with Charter,...