After a summit in Singapore on Tuesday, the two leaders signed an agreement to work towards the "complete denuclearisation" of the Korean Peninsula although observers say it is short on detail.
Mr Calvo said the agreement will end years of instability in Korea and the Pacific region.
He said the people of Guam have experienced suffering and death during World War Two and were the target of North Korean missile threats in 2013 and last year.
He said the promise of peace in the region was closer and said Guam's thankful for the president's stance.
"This agreement paves the way for peace between the U.S. and North Korea and moves us toward the denuclearization of the Korean peninsula," Mr Calvo said in a statement.
"The Territory of Guam is thankful to our President and his stance on peace through strength policy which elevated peace within the Asia Pacific region - this is something we truly are grateful for."