By amassing stakes in hundreds of companies, internet giant Tencent Holdings Ltd. of China has quietly become one of the world’s largest and most active technology investors, a calculated strategy that is crowding out rivals and bolstering its profits.

The social-media and videogame company has bought stakes in 277 startups since 2013 and its pace of deal-making accelerated last year, according to data from Dow Jones VentureSource. In 2017 alone, Tencent invested in more than 80 private and public companies, participating...