The government said 19 of the 24 bills outlined in the speech will apply in whole or in part to Scotland.
And the Scottish secretary said there will "undoubtedly" be more powers devolved to Edinburgh after Brexit.
But opposition parties said the general election result meant the Conservatives have no mandate to govern.
The SNP claimed that Theresa May was a "lame duck prime minister leading a lame duck government".
And Scottish Labour said the speech had set out a "weak, vague and mean-spirited programme from a government in meltdown".
Ms May - who lost her majority in the snap election earlier this month - has been forced to either axe or delay a number of key manifesto plans.
Much of what remained in the Queen's Speech related to Brexit, including the so-called Repeal Bill - which will copy all existing EU laws into UK law, with parliament then deciding which bits to retain.
The bill would give the UK Parliament temporary authority to amend laws that do not "operate appropriately" after Brexit.
And existing decision-making powers devolved to Scotland, Wales and Northern Ireland will be maintained pending further discussion on "lasting common frameworks".
Scottish Secretary David Mundell said the powers will be returned from Brussels "in a way that works best for Scotland and the rest of the UK".
He added: "There will undoubtedly be more decision-making powers coming to Holyrood, and I look forward to working closely with the Scottish government on this."
The Scottish government has repeatedly claimed that the prime minister is planning a "power grab" because she has not confirmed that all of the powers associated with devolved areas, such as fishing and agriculture, will be handed to Holyrood once they return from Brussels.
Ahead of what was a relatively low-key State Opening of Parliament, the prime minister promised to work with "humility and resolve" after failing to win the general election outright.
In an apparent sign of recognition that she must seek a broad consensus for any Brexit deal, Mrs May said getting EU withdrawal right will mean securing "a deal which delivers the result of last year's referendum and does so in a way that commands maximum public support".
The government used the Queen's Speech to stress that one of its priorities was to "build a more united country, strengthening the social, economic and cultural bonds between England, Northern Ireland, Scotland and Wales".
And Mrs May said her programme for government would include measures to support the aerospace industry in Wales, protect access to British waters that are "so important to Scottish fishermen", and open new markets for key exporting industries in Northern Ireland.
She said: "So this is a government with purpose. Determined to deliver the best Brexit deal, committed to keeping our country safe, enhancing our standing in the wider world and bringing our United Kingdom closer together."
The Queen had earlier been accompanied by the Prince of Wales, rather than the Duke of Edinburgh, for the ceremony.
Prince Philip was admitted to hospital on Tuesday night as a "precautionary measure" for treatment of an infection arising from a pre-existing condition.
Conservative ministers are still attempting to secure a deal with the DUP, which would see the Northern Irish party support Mrs May's minority government.
As well as the bill to convert EU rules into UK law, the government unveiled measures on trade, customs, immigration, fisheries, agriculture, nuclear and sanctions.
On immigration, a bill will legislate for the end of free movement from the EU and make the status of EU nationals and family members subject to UK law.
Although there are no specific details about a new system, ministers say they will be able to "control" numbers while attracting the "brightest and the best".
A Fisheries bill will allow the UK to take on responsibility for "access to fisheries and management of its waters".
And an Agriculture Bill will "provide stability" for farmers and ensure an "effective system" of support to replace the Common Agricultural Policy.
Ian Blackford, the SNP's new leader at Westminster, said there was "nothing in the programme to try and turn around the faltering economy, or how to support our under-pressure public services".
He added: "No one can have any confidence in this Tory government's ability to speak on Scotland's behalf in the vital Brexit negotiations - this makes it all the more vital that Scotland is given a seat at the negotiating table."
Shadow Scottish Secretary Lesley Laird said the government's proposals failed to reflect the message that voters sent to Mrs May in the general election.
She said: "Theresa May has no political authority, and while she struggles to stitch together a deal with the DUP to stay in office, she has been forced to ditch policies from her wildly unpopular manifesto."
The Liberal Democrats said the Queen's Speech was "bereft" of ideas to support public services.
The prime minister has pledged to bring the United Kingdom "closer together" as her government unveiled its proposed new laws in the Queen's Speech.