The 1963 NFL season was the 44th regular season of the National Football League. On April 17, NFL commissioner Pete Rozelle indefinitely suspended Green Bay Packers running back Paul Hornung and Detroit Lions defensive tackle Alex Karras for gambling on their own teams, as well as other NFL games; Hornung and Karras would miss the entire season. In addition, five other Detroit players were fined $2,000 each for placing bets on one game in which they did not participate.
The season ended when the Chicago Bears defeated the New York Giants in the NFL Championship Game. Taken from https://en.wikipedia.org/wiki/1963_NFL_season

The 1963 American Football League season was the fourth regular season of the American Football League.
The season ended when the San Diego Chargers defeated the Boston Patriots in the AFL Championship game – to this date the only major league championship won by the Chargers and the city of San Diego. Taken from https://en.wikipedia.org/wiki/1963_American_Football_League_season

Final Stats:

NFL
Record	Team
11 1 2	Chicago Bears
11 2 1	Green Bay Packers
11 3	New York Giants
10 4	Cleveland Browns
9 5	St. Louis Cardinals
7 4 3	Pittsburgh Steelers
8 6	Baltimore Colts
5 8 1	Detroit Lions
5 8 1	Minnesota Vikings
5 9	Los Angeles Rams
4 10	Dallas Cowboys
3 11	Washington Redskins
2 10 2	Philadelphia Eagles
2 12	San Francisco 49ers
Playoff Games
Week	Day	Date		Winner/tie		Loser/tie	PtsW	PtsL
Champ	Sun	29-Dec	boxscore	Chicago Bears		New York Giants	14	10
AFL
Record	Team
11 3	San Diego Chargers
10 4	Oakland Raiders
7 6 1	Boston Patriots
7 6 1	Buffalo Bills
6 8	Houston Oilers
5 7 2	Kansas City Chiefs
5 8 1	New York Jets
2 11 1	Denver Broncos
Playoff Games
Week	Day	Date		Winner/tie		Loser/tie	PtsW	PtsL
Division	Sat	28-Dec	boxscore	Boston Patriots	@	Buffalo Bills	26	8
Champ	Sun	5-Jan	boxscore	San Diego Chargers		Boston Patriots	51	10