The move, which follows a similar promise to firms by George Osborne in his Autumn Statement last week, was welcomed by business leaders.
In a separate initiative designed to protect firms' competitiveness, Mr Swinney also announced the Scottish Government's small business bonus scheme would be extended, handing an extra 4000 firms a rates discount until 2016.
Unveiling his plans at Holyrood, Mr Swinney said matching England's rates cap would maintain a competitive advantage and make the country the best place to do business.
CBI Scotland's senior policy executive Laura McMahon said the rate would ensure the vast majority of Scottish firms were not put at a cost disadvantage compared with those in England.
Business leaders, however, joined the Scots Tories in criticising the Scottish Government's commitment to the large retail levy, which burdens supermarkets selling alcohol and tobacco.