How to specify prefix for all controllers in Spring Boot?

You can provide a mapping to root context path of your spring boot application to /api/* in your custom configuration.

import org.springframework.boot.autoconfigure.web.DispatcherServletAutoConfiguration;
import org.springframework.boot.context.embedded.ServletRegistrationBean;
import org.springframework.context.annotation.Bean;
import org.springframework.context.annotation.Configuration;
import org.springframework.web.servlet.DispatcherServlet;

@Configuration
public class DispatcherServletCustomConfiguration {

    @Bean
    public DispatcherServlet dispatcherServlet() {
        return new DispatcherServlet();
    }

    @Bean
    public ServletRegistrationBean dispatcherServletRegistration() {
        ServletRegistrationBean registration = new ServletRegistrationBean(
                dispatcherServlet(), "/api/");
        registration.setName(DispatcherServletAutoConfiguration.DEFAULT_DISPATCHER_SERVLET_REGISTRATION_BEAN_NAME);
        return registration;
    }
}

or add this to your application.properties in src\main\resources folder

server.contextPath=/api

EDIT

As of Spring Boot 2.x the property has been deprecated and should be replaced with

server.servlet.contextPath=/api

More you find here Spring Boot Context Root and here Add servlet mapping to DispatcherServlet