“It’s not every day you become a world champion,” 30-year-old Cilic said.
“For us it is a dream come true, for this country. It’s possible to observe the fans are enthusiastic and they are here enjoying themselves. In Croatia it is going to be incredible also.”
This is the last staging of the group contest in its current format until it changes next year.
Croatia won the contest in 2005.
Cilic’s success on Sunday supposed the inaugural match between Jo-Wilfried Tsonga and Borna Coric was a dead rubber.
While Chilic put Croatia 2-0 up by beating on Tsonga coric won his singles rubber against Jeremy Chardy.