How to use Redirect in the new react-router-dom of Reactjs

I am using the last version react-router module, named react-router-dom, that has become the default when developing web applications with React. I want to know how to make a redirection after a POST request. I have been making this code, but after the request, nothing happens. I review on the web, but all the data is about previous versions of the react router, and no with the last update.

Code:

import React, { PropTypes } from 'react';
import ReactDOM from 'react-dom';
import { BrowserRouter } from 'react-router-dom';
import { Redirect } from 'react-router'

import SignUpForm from '../../register/components/SignUpForm';
import styles from './PagesStyles.css';
import axios from 'axios';
import Footer from '../../shared/components/Footer';

class SignUpPage extends React.Component {
  constructor(props) {
    super(props);

    this.state = {
      errors: {},
      client: {
        userclient: '',
        clientname: '',
        clientbusinessname: '',
        password: '',
        confirmPassword: ''
      }
    };

    this.processForm = this.processForm.bind(this);
    this.changeClient = this.changeClient.bind(this);
  }

  changeClient(event) {
    const field = event.target.name;
    const client = this.state.client;
    client[field] = event.target.value;

    this.setState({
      client
    });
  }

  async processForm(event) {
    event.preventDefault();

    const userclient = this.state.client.userclient;
    const clientname = this.state.client.clientname;
    const clientbusinessname = this.state.client.clientbusinessname;
    const password = this.state.client.password;
    const confirmPassword = this.state.client.confirmPassword;
    const formData = { userclient, clientname, clientbusinessname, password, confirmPassword };

    axios.post('/signup', formData, { headers: {'Accept': 'application/json'} })
      .then((response) => {
        this.setState({
          errors: {}
        });

        <Redirect to="/"/> // Here, nothings happens
      }).catch((error) => {
        const errors = error.response.data.errors ? error.response.data.errors : {};
        errors.summary = error.response.data.message;

        this.setState({
          errors
        });
      });
  }

  render() {
    return (
      <div className={styles.section}>
        <div className={styles.container}>
          <img src={require('./images/lisa_principal_bg.png')} className={styles.fullImageBackground} />
          <SignUpForm 
            onSubmit={this.processForm}
            onChange={this.changeClient}
            errors={this.state.errors}
            client={this.state.client}
          />
          <Footer />
        </div>
      </div>
    );
  }
}

export default SignUpPage;