Pre-event favourite Tennis player Andy Murray won the award ahead of Rugby League player Kevin Sinfield and heptathlete Jessica Ennis-Hill in third. Controversial boxer Tyson Fury placed fourth.
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It’s the second time that Murray has won the award – he also took it in 2013 after winning Wimbledon.
Of the 12 nominees, Froome placed sixth with a 3.87 per cent share of the vote and Armitstead tenth with 2.21 per cent of the 1,009,498 votes cast by the public.
Froome was absent from the live show as his partner Michelle gave birth to their son, Kellan, last week. Armitstead was present with partner and Team Sky professional Philip Deignan, who according to Armitstead had been hit by a car the previous day and was sporting a sling for his right arm.
Murray’s votes accounted for 35 per cent of all those cast during a phone and internet vote during the SPOTY show’s live broadcast from the SSE Arena in Belfast, Northern Ireland.
The other nominees were Lucy Bronze (football), Mo Farah (athletics), Lewis Hamilton (Formula 1), Adam Peaty (swimming), Greg Rutherford (athletics), and Max Whitlock (gymnastics).
Watch: Best of the 2015 Tour de France
Four cyclists have won the award in its history, three of them in the last decade. Tom Simpson was the first in 1965, then Chris Hoy won it in 2008, Mark Cavendish in 2011 and Bradley Wiggins in 2012.
Froome became the first British rider in history to win two editions of the Tour de France, and Armitstead dominated the 2015 women’s race season with overall victory in the UCI World Cup and road race world championship.