Britain's biggest retailer said the cash and shares deal, originally worth £3.7bn when it was first revealed in January 2017, was implemented through a court-sanctioned scheme of arrangement.
The move followed approvals by both sets of shareholders at meetings last Wednesday and regulatory approval from the Competition and Markets Authority back in December.
According to Sky News, 83.4% of Booker investors approved the deal last week, well above the 75% needed to go ahead.
Meanwhile 85.22% of Tesco shareholders voted for the takeover to proceed, with 14.78% of votes opposing it. Tesco had needed 50% support from shareholders.
Dave Lewis, Tesco’s group chief executive said after the shareholders votes: "I'm delighted that the shareholders of both companies have supported the merger.
"This merger is about growth, bringing together our complementary retail and wholesale skills to create the UK's leading food business.”