Here are some key lines from the nominees' remarks in Delaware:
Antony Blinken, Secretary of State nominee
Blinken said that the US needs to proceed "with equal measures of humility and confidence" in working with other countries because "we can't solve all of the world's problems alone."
"We need to be working with other countries, we need their cooperation. We need their partnership," he said.
Blinken said the US has a "greater ability than any other country on Earth to bring others together to meet challenges of our time."
Alejandro Mayorkas, Homeland Security Secretary nominee
Mayorkas, who would become the first Latino to helm the department if confirmed, said that the Department of Homeland Security has "a noble mission, to help keep us safe and to advance our proud history as a country of welcome."
Avril Haines, Director of National Intelligence nominee
Haines, who would become the first woman to lead the US intelligence community, said that Biden knows she has "never shied away from speaking truth to power," adding, "that will be my charge as director of national intelligence."
"I worked for you for a long time and I accept this nomination knowing that you would never want me to do otherwise and that you value the perspective of the intelligence community and that you will do so even when what I have to say may be inconvenient or difficult, and I assure you, there will be those times."
Linda Thomas-Greenfield, UN Ambassador nominee
Thomas-Greenfield, who has worked for 35 years in foreign service across four continents, said she likes to put a "cajun spin" on diplomacy.
"I called it gumbo diplomacy. Wherever I was posted around the world, I'd invite people of different backgrounds and beliefs to help me make a roux, chop onions for the holy trinity, and make homemade gumbo."
She added: "It was my way of breaking down barriers, connecting with people, and starting to see each other on a human level."
Jake Sullivan, National Security Adviser nominee
Sullivan noted that he served as Biden's national security adviser when he was vice president.
"I learned a lot about a lot, about diplomacy, about strategy, about policy. Most importantly about human nature. I watched him pair strength and resolve with humanity and empathy."
On Biden, he added, "That is the person America elected. That's also America at its best."
John Kerry, Climate Envoy nominee
Kerry said that in the fight against climate change "failure is not an option."
"Succeeding together means tapping into the best of American ingenuity, creativity, diplomacy, from brain power to alternative energy power, using every tool we have to get where we have to go," he said.
Kerry added: "No one should doubt the determination of this president and vice president, they shouldn't doubt the determination of the country that went to the moon, cured supposedly incurable diseases, and beat back global tyranny to win World War II."