Moore was publicly backed by president Donald Trump, but his campaign was marred by allegations that he sexually abused teenage girls more than three decades ago.
Accusations he denies.
Striking an unusually magnanimous tone, president Trump tweeted his congratulations to Jones, saying it had been a hard fought race.
The loss of what should have been a safe senate seat will come as a huge blow to president Trump.
The republicans will now have a slender two seat majority in the upper house.
Our US correspondent Philip Crowther in Alabama says this is a huge blow for Trump and and the biggest upset in US politics since the election of the president himself.