composer.json

{
    "name": "your/package",
    "type": "typo3-flow-package",
    // ...
    "require": {
        "raven/raven": "*"
    },
    // ...
}

SentryExceptionHandler.php

<?php
namespace Your\Package\Error;

/*                                                                        *
 * This script belongs to the TYPO3 Flow package "Your.Package".          *
 *                                                                        *
 *                                                                        */

use TYPO3\Flow\Error\ProductionExceptionHandler;

/**
 * Production Exception handler that reports exceptions to a configurable Sentry DSN using the raven library
 */
class SentryExceptionHandler extends ProductionExceptionHandler {

	/**
	 * @param \Exception $exception
	 * @return void
	 */
	protected function echoExceptionWeb(\Exception $exception) {
		if (isset($this->options['sentryDsn']) && strlen($this->options['sentryDsn']) > 0) {
			$ravenClient = new \Raven_Client($this->options['sentryDsn']);
			$ravenClient->captureException($exception);
		}
		parent::echoExceptionWeb($exception);
	}
}

Settings.yaml

TYPO3:
  Flow:
    error:
      exceptionHandler:
        className: 'Your\Package\Error\SentryExceptionHandler'
        # Sentry DSN (e.g. "http://public:secret@example.com/1")
        'sentryDsn': ''