Ms Ardern said she hopes to see a more "settled world" with Joe Biden in the Oval Office, nearly 12 weeks after he was first declared winner of the 2020 election.
Her comments came after Mr Biden signed executive orders (EO) to repeal Mr Trump's travel ban on Muslim countries and rejoined the Paris Climate Agreement (PCA) on his first day as president.
Speaking to reports in Nelson on Thursday, Ms Ardern remained diplomatic when referring to the outgoing president, but suggested her government will form much closer ties with the Biden administration.
She said: "Our job has always been to make it work on behalf of our countries. It is obviously a lot easier to do that when you have a few more shared values."
Asked to describe Mr Trump's term in office, Ms Ardern said: "There is no question. The history books will tell us it has been tumultuous."
She is among a number of world leaders to congratulate Mr Biden on his inauguration, which brought an end to one of the most chaotic periods in American history.
Speaking in front of a vacant but heavily militarised National Mall on Wednesday afternoon, Mr Biden declared that "democracy has prevailed" in a veiled attack on his predecessor.
He later called on Republicans and Democrats to come together to overcome the country's challenges and "restore the soul and secure the future of America".
"The United States is back," European commission leader Ursula von der Leyen said of Mr Biden's swearing-in.
"And Europe stands ready. To reconnect with an old and trusted partner, to breathe new life into our cherished alliance. I look forward to working together with Joe Biden," she added.
There were performances from pop stars Lady Gaga and Garth Brooks, who together sang the national anthem. Jennifer Lopez also performed a mixture of songs.
Later in the day, the new commander-in-chief issued a flurry of EO's aimed at dismantling Mr Trump's legacy.
“There's no time to start like today,” the new president said from the Oval Office Resolute Desk.
As well as overturning Mr Trump's Muslim travel ban and resigning the PCA, Mr Biden introduced a Covid mask mandate and a pledge to provide immediate financial relief to the millions of Americans who have lost their jobs due to the pandemic.