With Spring Boot 2.x, all it takes is a single property in application.properties:
server.servlet.context-path=/api
With Spring Boot 1.2+ (<2.0)
spring.data.rest.basePath=/api
ref link : https://docs.spring.io/spring-data/rest/docs/current/reference/html/#getting-started.changing-base-uri

With Spring Boot 1.2+ (<2.0) all it takes is a single property in application.properties:

spring.data.rest.basePath=/api
ref link : https://docs.spring.io/spring-data/rest/docs/current/reference/html/#getting-started.changing-base-uri
For 2.x, use
server.servlet.context-path=/api