Speaking to The Times, he pledged to deliver on the goals of Johnson, but end a period of "often-distracted" government.
He also said he was "determined" to address the cost of living crisis in the UK and rebuild the economy so it is the biggest in Europe by 2050.
Shapps said he would hold an emergency budget in his first 100 days in office, instructing his chancellor to cut personal tax for the "most vulnerable" and giving state support to firms with high energy consumption.
"I have not spent the last few turbulent years plotting or briefing against the prime minister," he added. "I have not been mobilising a leadership campaign behind his back. I tell you this: for all his flaws – and who is not flawed – I like Boris Johnson."
"Even as the skies darkened over his premiership, often because of errors committed by him, I hoped he could pull it back. Because in losing him we would lose a man who makes a unique connection with people."
He further emphasised his leadership would return to a more "traditional" style of government and an "old-school" Conservative approach towards the state.