Opener Mark Stoneman scored the winning boundary to secure Durham's third title in six years after successive triumphs in 2008 and 2009.
Durham, bottom of the Division One table in July last year, started the season with a 2.5-point penalty as punishment for breaking salary cap rules.
In mid-June, head coach Geoff Cook suffered a major heart attack while jogging but surprised his players by returning to the team last month.
"It is just fantastic that he came through that and I know every single man in that dressing-room was doing it for Geoff," captain and former England batsman Paul Collingwood told Sky Sports.
Durham had resumed on 7-0, needing another 62 runs, after rain delayed the start of the third day's play.
Harry Gurney took two wickets for Nottinghamshire but Stoneman saw Durham home and finished on 35 not out.
Durham, enjoying their fifth win in a row, bowled out the visitors for 78 on the opening day. They looked in trouble at 45 for five in their first innings before recovering to score 256, helped by a 121-run partnership between Collingwood (88 not out) and Phil Mustard (77).
Notts had a better second innings but their score of 246 left a target of only 69 for Durham who are England's youngest first-class county having gained that status in 1991.
- Sports & Recreation
- Paul Collingwood