Lampard's uncle Harry Redknapp, the Tottenham manager, was also under consideration.
He told The Sun: "I really love the feel of Roy's England. It's brilliant.
"It's a far more relaxed atmosphere and that's a big change from the regime before.
"There's plenty of down time where everyone can switch off and do their own thing. But training is very focused and intense.
"He wants training to be at the top level, he wants everyone to be at it. He's definitely very strict on getting it right and very keen on getting his message across.
"You quickly realise how good he is. He has so much experience that he's picked up from working all around the world."