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The 25-year-old right-hander heard the good news during the lunch break of what was to become Otago's nine-wicket loss to Northern Districts in Alexandra on Saturday.
"I've sort of been dreaming about this day for the last couple of years and to be named is awesome," Broom said.
"I'm a wee bit nervous. But I'm playing for Otago again [tomorrow], so I'll get a bit more batting in then, and I'm looking forward to Queenstown."
The five-match one-day series is scheduled to get under way in Queenstown on Wednesday, with the second match in Christchurch on January 3.
Broom will play for Otago against Central Districts in Alexandra tomorrow and then join the Black Caps for the match in Queenstown.
He was promoted to the national squad to replace Scott Styris, who broke his thumb during the twenty/20 match against the West Indies on Boxing Day.
There are two other changes from the twenty/20 side, with Grant Elliott and Jamie How also coming into the 13-strong squad.
Broom played alongside the likes of Ross Taylor and Jesse Ryder in New Zealand age group teams and has long been singled out as a player with enormous potential.
National selector Glenn Turner said Broom had demonstrated his ability to make the step up to international cricket with good performances with the bat in Australia and India with the Emerging Players and New Zealand A sides.
"He's also been scoring a lot of runs in the State Championship this summer," Turner said.
Broom has scored 382 runs at an average of 63.66 in the championship this season, including an undefeated 140 and three 50s.
"I'm pretty pleased with my first-class form.
''I've been hitting it pretty well.
''I missed out the other day [during the one-day match against Northern Districts in Alexandra] but I'm looking forward to playing CD and hopefully getting a few more runs under my belt."
Broom, who started his career with Canterbury, shifted south to Otago for the 2005-06 season and in 28 matches since has built an impressive batting record, averaging just under 44.