Baker will take up his new role as chief executive of the high street retailer and chemist from September 15.
Current CEO at Boots, Steve Russell, will leave the board at the end of May.
Boots has also appointed Sir Nigel Rudd as chairman with effect from September 15.
He will succeed John McGrath who will takeover from Russell at the end of May until September 15 when he will retire from the board.
McGrath said: "We have been looking for the right person to accelerate strategic change at Boots.
“I believe that with Sir Nigel Rudd as chairman and Richard Baker as chief executive we have an excellent combination of skills to lead our strong new executive team."