MSPs are to take over control of stamp duty when the Land and Buildings Transactions Tax (LBTT) is expected to be passed by a vote in parliament.
It means the Scottish Parliament will set and collect a proportion of the revenue it spends for the first time.
Holyrood does have the power to vary income tax by 3 pence – the so-called tartan tax – but this has never been used.
Mr Swinney said: “With parliament’s approval the passing of this bill will be a huge milestone for Scotland – it will enable us to set and collect taxes in a more cost effective and fairer way than the UK government.
“This bill will give us the opportunity to better support first-time buyers.”