Twitter Inc. TWTR 5.66% on Monday accepted Elon Musk’s bid to take over the company, which would give the world’s richest man control over the social-media network where he is also among its most influential users.

The $44 billion deal marks the close of a dramatic courtship and a change of heart at Twitter, where many executives and board members initially opposed Mr. Musk’s takeover approach. The deal has polarized Twitter employees, users and regulators over the power tech giants wield in determining the parameters of acceptable discourse on the internet and how those companies enforce their rules.

The two sides worked through the night to hash out a deal in which Mr. Musk plans to take Twitter private.