He was named to the Second All-Star Team in 2015-16 after recording nine goals and 20 assists in 47 games with Tappara's Under-20 junior club in Finland.
"As well as having that size and ability to defend using his size and reach, we feel there is a little more un-tapped offensive dimension there in his game".
Ten of the top 13 picks were listed as centers.
Commissioner Gary Bettman was booed as he took the podium to begin the night, but seemed underwhelmed by the response he got.
After dealing Niklas Hjalmarsson, Artemi Panarin and Tyler Motte before lunch, the Hawks swapped first round picks with the Dallas Stars, moving back from 26th to 29th to select Henri Jokiharju.
"It's an awesome feeling, of course, Jonathan Toews and Patrick Kane calling my name".More news: Minneapolis police asked to limit presence at pride parade
Jokiharju, 18, paced all WHL rookie defensemen with 48 points (9G, 39A) and four power-play goals in 71 regular-season games this past season.
The 18-year-old Altybarmakyan is from St. Petersburg, Russia. New Jersey is coming off its worst season in almost three decades, finishing with a 28-40-14 record.
"I love hockey", he said.
The Winterhawks' have a rich tradition of producing talent for the NHL Draft, with 137 players now having been selected in the NHL Draft in franchise history.
The 18-year-old Patrick, a Winnipeg, Manitoba, native whose father Steve and uncle James played in the NHL, held the top spot in the NHL Central Scouting Department's final rankings in April.
The New York Rangers and Tampa Bay Lightning also opted for players with family ties to the National Hockey League. Callan Foote, who went to Tampa Bay at No. 14, is the son of two-time Stanley Cup champion Adam Foote.