The Scotland Act includes powers over income tax, air passenger duty, abortion law and benefits.
Scottish Secretary David Mundell said the passage of the act marked a "truly significant day".
Nationalist MPs warned that in future they do not want to be "given crumbs from the table at Westminster".
Mr Mundell said: "It provides even greater opportunities for the Scottish Government to tailor and deliver Scottish solutions to Scottish issues.
"The Scottish Parliament that returns in May will be a powerhouse parliament that has come of age."
SNP representatives were less impressed.
Angus MacNeil, who represents Na h-Eileanan an Iar, said: "Isn't it time that we moved away from the devolution that is effectively crumbs from the table from Westminster and moved to a model that Copenhagen shares with the Faroe Islands and Greenland: The larder is open, you choose your own powers.
"No longer should we be given crumbs from the table at Westminster but the Scottish government takes the powers the Scottish government wants from Westminster when it wants."
Ian Murray, the shadow Scottish Secretary and Labour's only MP in Scotland, said: "With the passing of this bill and the dissolution of the Scottish Parliament we can lay the old arguments of the referendum to rest alongside any doubt that The Vow has not been delivered.
"The conversation must now move on to how these powers are used, or not used in some cases."
The Scotland Bill was passed by the Commons unopposed and became the Scotland Act after receiving the Royal Assent.
Legislation handing handing new powers to the Scottish parliament at Holyrood has cleared its final hurdle in the House of Commons.