He said revenue from energy production would be used to pay for rebuilding roads, bridges, schools and other crumbling infrastructure, and doing so would increase wages by more than US$30 billion ($42b) over the next seven years.
Trump had previously indicated that he would consider Monday "day one" of his administration. But he appeared to have decided to hit the ground running, saying he was keen to "get the show going".
Only an hour after finishing his inaugural address he signed his first three official orders.
They were a proclamation for a "National Day of Patriotism", a formal document that will allow General James Mattis to serve as defence secretary and a paper bearing formal nominations to the Senate.
Repealing Obamacare, immigration controls, efforts to defeat Isis (Islamic State), and strictures on lobbying in Washington, were also high on his list of priorities.
Aides said Mr Trump was still working through exactly which orders to sign but there was expected to be a frenzy of activity over the next five days.
Republican Party officials said they expected several executive orders relating to repealing Obamacare almost immediately.
An official at the department of health said they were "nervous", adding: "I don't know what we're rolling out on Monday."
Trump also began using his Twitter account to make announcements minutes after finishing his inaugural address, promising to give power "back to the people".
"This will be remembered as the day the people became the rulers of this nation again. The forgotten men and women of our country will be forgotten no longer," he wrote.
As part of his populist platform, Trump promised to deliver a US$1 trillion programme to rebuild infrastructure, and is considering US$10.5 trillion cuts to government spending over a decade. Immigration was central to his campaign, when he vowed to build a "beautiful" wall and "make Mexico pay for it".
