Swain will be responsible for leading the Knowledge strategy across all BBC factual programming, including arts, music, history, natural history, business, science, religion, consumer journalism and contemporary factual.
She has been acting controller of Knowledge commissioning since February, when Entwistle became temporary director of BBC Vision following Jana Bennett's departure to BBC Worldwide. Entwistle was officially appointed to the role in April.
Swain was previously head of Knowledge TV commissioning, overseeing an eight-strong team that commissions factual TV content from Vision Productions and the independent sector for the four BBC channels.
"Emma is one of the foremost creative leaders in factual television in the UK, passionate about programming, courageous in the way she embraces new ideas and respected by in-house producers and independents alike," said Entwistle.
"As acting controller, Emma has led the Knowledge commissioning team with great energy and skill and I'm delighted to confirm her permanently in the role."
Swain added: "The BBC produces the best factual programmes in the world and it's a great privilege to be given this role, with responsibility for maintaining the high standards and quality of Knowledge output that our viewers have come to expect.
"It's a tribute to our suppliers and to the great team of factual commissioners that Knowledge programming has both increased its reach and audience appreciation across all four channels in the last year, and I look forward to continuing to lead this great momentum."
Over her BBC career Swain has held a number of senior posts, including commissioning editor for specialist factual, head of Knowledge multimedia commissioning and head of Knowledge TV commissioning. She also spent a brief period in 2007 as acting controller of BBC Three.
She has helped develop a range of successful factual shows, including Don't Tell The Bride, Kill It Cook It Eat It, Comic Relief Does Kilimanjaro and Life.
Her former role as head of Knowledge TV commissioning will not be filled, as some of the responsibilities have already been redistributed.