The moves come as part of a major reshuffle by Prime Minister David Cameron Tuesday morning.
Fallon joined the Department of Energy and Climate Change (Decc) in June 2013, whilst already holding the role of business minister, and has now been confirmed as the new defence secretary.
Barker, who has been a prominent green Tory, had been in his post since the 2010 election, but announced via twitter he was standing down from Decc.
He also announced he would not be standing for re-election in next year’s general election.
Cameron also announced that Hastings and Rye MP Amber Rudd would be joining Decc as the climate change minister, replacing Barker.
Rudd was elected in May 2010, and she was previously Parliamentary Private Secretary to the Chancellor of the Exchequer George Osborne between September 2012 and October 2013.
The environment secretary Owen Paterson, who had been in the post since 2012, was another victim of Cameron’s reshuffle.
He was replaced by the former education minister Liz Truss, who will now head up the Department for Environment, Food, and Rural Affairs (Defra).
The South West Norfolk MP was elected in 2010 and was a member of the justice committee between 2010 and 2012.
Truss is not a supporter of large scale solar farms, having expressed her concerns in April this year about the impact they have on green field sites and on agricultural land.
She said: “There are so many more options for the sitting of solar panels, for example utilising existing industrial locations and commercial premises, not to mention residential roofs.”
Truss has also voiced concerns about the impact of biomass plants on the rural economy.
In January last year, she said: “I am keen to ensure that prime agricultural land is not lost to fuel production.”
Reacting to Paterson’s departure, Greenpeace executive director John Sauven said: “If history remembers him, it will not be kind.
“An ideological attachment to climate change denial saw him sack people working on flood defences just when we needed them most.
“When his own scientists tried to brief him, he refused to hear them out.
“Hopefully his successor will have an affinity for evidence-based policy-making. Mr. Patterson most certainly did not.”
The deputy prime minister and Liberal Democrat leader, Nick Clegg, is expected to announce his own reshuffle after the summer recess but energy secretary Ed Davey is expected to remain in his post.