The deal continues a shake-up of the engineering services industry, following Jacobs' $3.3 billion (2.5 billion pounds) purchase of rival CH2M Hill Cos Ltd last year and the 2.2 billion pound takeover of Amec Foster Wheeler by UK oilfield services firm John Wood Group.
It comes as WorleyParsons emerges from a three-year downturn following the oil price crash, and positions it to tap growth in the refining and petrochemical sectors, with countries like India building massive new plants.
"Hydrocarbons and minerals and metals are both coming off the bottom and are well below their peaks of 2013. We think this is an exciting time for the sector," WorleyParsons Chief Executive Andrew Wood told analysts on a conference call.
Jacobs, the largest service provider to the NASA space programme, said it would now focus on higher growth, higher margin lines of business including aerospace, technology and nuclear projects as well as buildings and infrastructure.
The acquisition would make WorleyParsons the world's biggest provider of professional services in energy and resources, it said, with a large footprint in Europe and North America, complementing its exposure in the Middle East and Asia.
The transaction will also expand its exposure to the refining and petrochemicals sectors, which Wood said was appealing as the revenue streams are less volatile than oil and gas exploration and production, where WorleyParsons is already a leader.
The deal would double the company's 2018 earnings before interest, tax, depreciation and amortisation (EBITDA) on a proforma basis to A$735 million (400.40 million pounds), and boost its earnings per share by 50 percent after achieving savings of A$130 million, Wood said.
Jacobs said it would receive $2.6 billion in cash plus $700 million worth of shares giving it an 11 percent stake in the enlarged WorleyParsons.
"For Jacobs, this transaction marks an inflection point in our portfolio transformation focussed on more consistent, higher-margin growth as a leader solving the world's critical challenges," Jacobs Chairman and Chief Executive Steve Demetriou said in a statement.
The deal has been approved by both boards and is expected to close in the first half of 2019.
WorleyParsons plans to fund the deal via a A$2.9 billion entitlement offer plus the share issue to Jacobs and new debt.
The issue to Jacobs will be priced at A$16.92 a share. The rest of the offer would be priced at A$15.56 a share, a 13 percent discount to WorleyParsons' close last Friday. WorleyParsons founder and chairman John Grill, the company's second-largest shareholder, will be tipping in A$100 million.
UBS, which advised WorleyParsons on the deal, is joint lead manager with Macquarie Capital on the share sale.
Perella Weinberg Partners LP is financial adviser to Jacobs.
(Reporting by Sonali Paul and Jessica Resnick-Ault; editing by Sandra Maler and Richard Pullin)
By Sonali Paul and Jessica Resnick-Ault