RouteObserver

main.dart

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      theme: ThemeData(),
      navigatorObservers: [MyRouteObserver()],
      home: Screen1(),
      routes: {
        '/screen1': (context) => Screen1(),
        '/screen2': (context) => Screen2(),
        '/screen3': (context) => Screen3(),
      },
    );
  }
}

class MyRouteObserver extends RouteObserver<PageRoute<dynamic>> {
  void _sendScreenView(PageRoute<dynamic> route) {
    var screenName = route.settings.name;
    print('screenName $screenName');
    // do something with it, ie. send it to your analytics service collector
  }

  @override
  void didPush(Route<dynamic> route, Route<dynamic> previousRoute) {
    super.didPush(route, previousRoute);
    if (route is PageRoute) {
      _sendScreenView(route);
    }
  }

  @override
  void didReplace({Route<dynamic> newRoute, Route<dynamic> oldRoute}) {
    super.didReplace(newRoute: newRoute, oldRoute: oldRoute);
    if (newRoute is PageRoute) {
      _sendScreenView(newRoute);
    }
  }

  @override
  void didPop(Route<dynamic> route, Route<dynamic> previousRoute) {
    super.didPop(route, previousRoute);
    if (previousRoute is PageRoute && route is PageRoute) {
      _sendScreenView(previousRoute);
    }
  }
}

class Screen1 extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(
        child: RaisedButton(
          color: Colors.pink.shade200,
          child: Text('GOTO Screen 2'),
          onPressed: () => Navigator.of(context).pushNamed('/screen2'),
        ),
      ),
    );
  }
}

class Screen2 extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(
        child: RaisedButton(
          color: Colors.blue.shade200,
          child: Text('GOTO Screen 3'),
          onPressed: () => Navigator.of(context).pushNamed('/screen3'),
        ),
      ),
    );
  }
}

class Screen3 extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(
        child: RaisedButton(
          color: Colors.yellow.shade200,
          child: Text('GOTO Screen 1'),
          onPressed: () => Navigator.of(context).pushNamed('/screen1'),
        ),
      ),
    );
  }
}