More than 2,000 people die from smoking-related illnesses in Northern Ireland every year.
Treating these conditions costs the NHS in Northern Ireland more than £200m, according to the Department of Health.
On vapes, he said the bill includes regulation-making powers to allow for future restrictions on vape flavours, packaging and point-of-sale displays.
The bill is progressing through Parliament despite opposition from several leading Tory figures.
The Democratic Unionist Party (DUP) also voted against the bill in the Commons, but said they plan to work on improving the legislation.
DUP assembly member Diane Dodds said it was “important that we are part of the UK-wide legislation”.
She added the bill “as drafted does have significant challenges” and her party’s MPs “will be working to try to use their influences”.
Mrs Dodds also questioned whether the bill would be affected by EU post-Brexit trade rules under the Windsor Framework.
Traditional Unionist Voice (TUV) leader Jim Allister told assembly members the Republic of Ireland and Denmark had been unable to introduce similar laws due to EU rules.
The Irish government is instead planning a ban on the sale of tobacco products for those aged under 21.
Mr Allister asked: “Here are two EU member states, and we are in the same pickle, who have said we can’t do it. Does that not concern the minister?”
Mr Swann said the issue “does concern me” but he added that “we have been assured by the UK government that no such barriers exist”.
The Ulster Unionist Party (UUP) minister said that “we remain unaware of any Windsor Framework barriers to the Northern Ireland application of the measures set out in this bill”.
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