Israel–Premier's Williams won the second and third stages earlier in the week to put himself in position to seal victory with a final time of 21 hours, 25 minutes and 14 seconds.
The 28-year-old finished 16 seconds ahead of Scotland's Oscar Onley to claim his third title in 13 months.
It was the first time since 2016 that a home rider lifted the Tour of Britain trophy.
Bahrain Victorious's Govekar finished the race on a high by taking the 158.4km stage from Lowestoft to Felixstowe.
The Slovenian held his nerve in a sprint finish ahead of Denmark's Rasmus Pedersen and Britain's Ben Swift.
France's Paul Magnier was aiming to equal the record of winning four individual stages in one Tour of Britain campaign.
But Magnier's crack at history ended prematurely when he had to abandon the final stage after suffering a fall with 35km left.
Stage six
1. Matevz Govekar (SLO/TBV) 3h 22min 18sec, 2. Rasmus Sojberg Pedersen (DEN/DAT) at same time, 3. Ben Swift (GBR/IGD) s.t., 4. Ethan Vernon (GBR/IPT) s.t., 5. Erlend Blikra (NOR/UXM) s.t.
Overal1 standings
1. Stephen Williams (GBR/IPT) 21h 25min 14sec, 2. Oscar Onley (GBR/DFP) at 16sec, 3. Tom Donnenwirth (FRA/DAT) at 36sec, 4. Mark Donovan (GBR/Q36) at 40sec, 5. Joe Blackmore (GBR/IPT) at 41sec