Lund, who joined Statoil in 2004, has grown the company exponentially over his 10-year tenure, boosting its market cap from 189 billion krone ($A32.8 billion) to more than 500 billion NOK.
Lund will join BG in March next year, ending a leadership crisis at the company which got rid of previous boss Chris Finlayson after little more than a year due to missed production growth targets.
The move could represent a tenfold increase in pay for Lund, making him Europe's best-paid oil company boss.
The remuneration outlined by BG guarantees the new boss £2 million ($A3.6 million) a year, but allows for raises based on performance targets, which could see that amount rise to £14 million.
Lund earned a base salary of $US1.15 million ($A1.3 million) last year at Statoil and a total package of $2.1 million.
BG apparently approached Lund six to eight weeks ago with its offer, which Lund took as a final opportunity for a "challenge".
"For leaders, there comes a time when it's right to move on, both for themselves and for the company they run," 52-year-old Lund said.
"I've wanted one more leadership challenge, I think I'm too young to retire. This is a challenge I find exciting, and that's the main motivation."
Lund's resignation has taken immediate effect, however, he will remain at the company's disposal until the end of his notice period on March 1.
Statoil's head of marketing, processing and renewables Eldar Saetre has taken up the interim position of CEO but has ruled himself out of the race for the permanent position.
A sub-committee has begun the search for a permanent replacement and will also engage with an external advisor.
"Helge's track record speaks for itself. He has built a world-class exploration and production portfolio at Statoil, and the company is now widely admired for its technical expertise, financial performance and strong, values-based culture," BG chairman Andrew Gould said.
"Helge is ideally suited to lead BG Group in the next phase of its growth, and to accelerate the creation and delivery of value for our shareholders, while delivering the group's business plans. The board and I are delighted to have secured his appointment.
"BG Group has excellent prospects. We will have strong production growth and cash generation over the coming years from our projects in Brazil and Australia.
"To make the most of this potential, we need to build on our strengths in exploration and LNG and also become a world-class operator.
"The company needs a proven leader from the oil and gas industry to deliver the exceptional opportunities available to it. We will be consulting with our shareholders and we are confident that they will be supportive."
Before taking up his post at Statoil, Lund cut his teeth as the CEO of Aker Kvaerner, before which he served in various executive roles at that company and with the pharmaceutical division of Hafslund Nycomed.
Lund is the first CEO to leave Statoil voluntarily.
