"The legacy of Teddy Kennedy can be measured by how we look at one another - and in turn how we look at ourselves," Biden said.
Biden also paid tribute to the help Kennedy paid to his own career, saying that he would not be where he is today without him.
Echoing a story he told on Wednesday about Kennedy coming to his aid during his 1972 Senate campaign, Biden said Kennedy was "the catalyst" for his victory.
Like many other speakers during the Friday night service, Biden then talked about hearing from Kennedy in his times of need, notably after his wife and daughter were killed in a car accident just weeks after he was elected.
"He took on the role of being my older brother," Biden said, talking about his early time in the Senate.
CBSNews.com Special Report: Ted Kennedy
CBS News Special Report: Ted Kennedy - The Last Brother
"He had an incredible impact on me, and I noticed everyone around him," Biden said.
The vice president also talked about Kennedy's impact in the Senate, saying that he other "act bigger."
"He made us all bigger -- his friends, his allies and his foes," Biden said. "His dignity, his lack vitriol, his lack of pettiness, forced some of the less generous members of our community to act bigger."
Biden added: "People didn't want to look small in front of him. Even the people who were small."
In his closing, he had a message for the next generation of the Kennedy family.
"Because of you, the dream still lives," Biden said.
Read more on tonight's memorial service on CBSNews.com:
Family, Political Luminaries Honor Kennedy
Caroline Kennedy: We Have to Do What He Would Have Done
Biden: Kennedy's Legacy Is How We Look at One Another
McCain: Senate "Won't Be the Same" Without Kennedy
Kerry: Kennedy's Gift Was "Incomparable Love of Life"
Hatch: Kennedy and I Were Like "Fighting Brothers"
Dodd: "Teddy Changed Our America"
Rep. Joseph Kennedy: Teddy Was Always There
Photos: The Scene at the JFK Library Memorial
Photos: Speakers Pay Tribute to Kennedy