Have you tried with a basic filter like this?

import java.io.IOException;
import javax.servlet.*;
import javax.servlet.annotation.WebFilter;
import javax.servlet.http.HttpServletRequest;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import org.springframework.stereotype.Component;

@Component
@WebFilter("/*")
public class StatsFilter implements Filter {

    private static final Logger LOGGER = LoggerFactory.getLogger(StatsFilter.class);

    @Override
    public void init(FilterConfig filterConfig) throws ServletException {
        // empty
    }

    @Override
    public void doFilter(ServletRequest req, ServletResponse resp, FilterChain chain) throws IOException, ServletException {
        long time = System.currentTimeMillis();
        try {
            chain.doFilter(req, resp);
        } finally {
            time = System.currentTimeMillis() - time;
            LOGGER.trace("{}: {} ms ", ((HttpServletRequest) req).getRequestURI(),  time);
        }
    }

    @Override
    public void destroy() {
        // empty
    }
}

EDITED: (Thanks @suren-aznauryan) Now, It uses Instant and Duration and avoids System.currentTimeMillis().

import java.io.IOException;
import java.time.Duration;
import java.time.Instant;
import javax.servlet.*;
import javax.servlet.annotation.WebFilter;
import javax.servlet.http.HttpServletRequest;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import org.springframework.stereotype.Component;

@Component
@WebFilter("/*")
public class StatsFilter implements Filter {

    private static final Logger LOGGER = LoggerFactory.getLogger(StatsFilter.class);

    @Override
    public void init(FilterConfig filterConfig) throws ServletException {
        // empty
    }

    @Override
    public void doFilter(ServletRequest req, ServletResponse resp, FilterChain chain) throws IOException, ServletException {
        Instant start = Instant.now();
        try {
            chain.doFilter(req, resp);
        } finally {
            Instant finish = Instant.now();
            long time = Duration.between(start, finish).toMillis();
            LOGGER.trace("{}: {} ms ", ((HttpServletRequest) req).getRequestURI(),  time);
        }
    }

    @Override
    public void destroy() {
        // empty
    }
}

Spring boot :logging interceptor

public class ApiLogger extends HandlerInterceptorAdapter {
  private static final Logger logger = LoggerFactory
    .getLogger(ApiLogger.class);

  @Override
  public boolean preHandle(HttpServletRequest request, HttpServletResponse response, Object handler) throws Exception {
    String requestId = UUID.randomUUID().toString();
    log(request,response, requestId);
    long startTime = System.currentTimeMillis();
    request.setAttribute("startTime", startTime);
    request.setAttribute("requestId", requestId);
      return true;
  }

  @Override
  public void afterCompletion(HttpServletRequest request, HttpServletResponse response, Object handler, Exception ex) throws Exception {
    super.afterCompletion(request, response, handler, ex);
    long startTime = (Long)request.getAttribute("startTime");    
    long endTime = System.currentTimeMillis();
    long executeTime = endTime - startTime;
    logger.info("requestId {}, Handle :{} , request take time: {}",request.getAttribute("requestId"), handler, executeTime);
  }

  private void log(HttpServletRequest request, HttpServletResponse response, String requestId) {
    logger.info("requestId {}, host {}  HttpMethod: {}, URI : {}",requestId, request.getHeader("host"),
      request.getMethod(), request.getRequestURI() );
  }
}

register interceptor :

@Configuration
@EnableWebMvc
public class AppConfig extends WebMvcConfigurerAdapter {
  @Override
  public void addInterceptors(InterceptorRegistry registry) {
    registry.addInterceptor(new ApiLogger()).addPathPatterns("/api/v1/*");
  }
}

Answer by David is correct - filter is a good way to implement such functionality in Spring Boot.

Spring Boot has a built-in endpoint which returns the information about last 100 requests like shown below:

[{
    "timestamp": 1394343677415,
    "info": {
        "method": "GET",
        "path": "/trace",
        "headers": {
            "request": {
                "Accept": "text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8",
                "Connection": "keep-alive",
                "Accept-Encoding": "gzip, deflate",
                "User-Agent": "Mozilla/5.0 Gecko/Firefox",
                "Accept-Language": "en-US,en;q=0.5",
                "Cookie": "_ga=GA1.1.827067509.1390890128; ..."
                "Authorization": "Basic ...",
                "Host": "localhost:8080"
            },
            "response": {
                "Strict-Transport-Security": "max-age=31536000 ; includeSubDomains",
                "X-Application-Context": "application:8080",
                "Content-Type": "application/json;charset=UTF-8",
                "status": "200"
            }
        }
    }
},{
    "timestamp": 1394343684465,
    ...
}]

If your application is calling another services or querying the database consider using Sniffy for profiling - it will show you not only time spent on your server but also time spent in calling downstream systems. See a live demo here (Check the black widget in top bottom corner).

Disclaimer: I'm the author of Sniffy