Barnes finished second on the 62km street race to move on to the podium as Belgium's Jolien D'Hoore won the stage, with Christine Majerus in third.
Luxembourg's Majerus finished second overall, 1:18 minutes behind Niewiadoma
Barnes' sister Alice was sixth with fellow Briton Dani King in ninth.
Britain's defending champion Lizzie Deignan finished 42nd overall, while Olympic team pursuit champion Katie Archibald was 18th.
1. Jolien D'Hoore (Bel/Wiggle High5) 1hr 28mins 23secs
2. Hannah Barnes (GB/Canyon SRAM Racing) same time
3. Christine Majerus (Lux/Boels Dolmans) same time
4. Roxane Fournier (Fra/FDJ) same time
5. Katie Archibald (GB/WNT) same time
1. Katarzyna Niewiadoma (Pol/WM3 Pro Cycling) 16hrs 34mins 53secs
2. Christine Majerus (Lux/Boels Dolmans) +1min 18secs
3. Hannah Barnes (GB/Canyon SRAM Racing) +1min 30sec
Britain's Hannah Barnes finished third on the Women's Tour as Poland's Katarzyna Niewiadoma claimed the overall title after Sunday's final stage in London.