Speaking after the vote, Deputy Prime Minister and Liberal Democrat Leader Nick Clegg said:
"I am delighted Simon has been elected as deputy leader.
"Simon has been a huge figure in the Liberal Democrats for decades. He's a tireless campaigner, a relentless fighter for the vulnerable and marginalised in our society, and one of the hardest working MPs Parliament has ever seen.
"There are huge challenges and opportunities ahead for our country and our party, but with Simon by my side I am sure that we can meet those challenges and work to build a fairer, more equal Britain."
Liberal Democrat Deputy Leader Simon Hughes said:
"It is an honour and a privilege for me to follow Vince Cable as the new Deputy Leader of the Liberal Democrats. This is not a responsibility I will ever take lightly.
"I will fight every day for the principles which underpin our party: fairness, freedom, openness, equality, stewardship of our environment and standing up for those who cannot stand up for themselves.
"I will work tirelessly with Nick Clegg and all other Liberal Democrats to help liberal democracy blossom and flourish throughout the land."
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