Hellberg has led the Stockholm team to two consecutive second places in the Allsvenskan during his two seasons at Hammarby. The 37-year-old is bringing his assistant coach David Selini to England for the job at "Boro".
"There are many things that make Boro the perfect choice for me. The team's playing style and game idea, together with the crowd, suits me and how I want to work," says Hellberg, who also coached IFK Värnamo in the Allsvenskan for two seasons.
Middlesbrough are second in the second-highest division after 16 games played. The club has not played in the Premier League since 2016–2017.
Hellberg will take over the team later this week. On Tuesday, Middlesbrough have a home game against Coventry in the league, but the team will then be led by assistant coach Adi Viveash.
The club lost its head coach Rob Edwards to Premier League club Wolverhampton last week.
