I’m delighted that you’re coming to China as an exchange student 

我很高兴你以交换生的身份来到中国

that you are coming to China as an exchange student为原因状语从句,用来说明主语be delighted的原因。可以理解为“because you are coming to China as an exchange student”

主语+系动词be+（喜怒哀乐等情感的形容词）+that 从句，从句说明情感的原因

I am very sorry that I woke you up. 很抱歉把你吵醒了。

I’m sorry that you should have to leave. 我很遗憾，你得走了。

I’m sorry that I’ve delayed so long. 我很抱歉拖了这么久。

I’m sorry that I have to bother you with [about] this problem. 对不起，我要用这个问题来麻烦你了。

I am glad you are beginning to see it. 我很高兴你慢慢认识到了这一点。

I’m so happy that you could visit us. 我很高兴你能来看望我们。

He was so ashamed that he hid his face in his hands. 

他羞愧得用手把脸蒙住。

英语中，be + adj. + that... 结构 根据作表语形容词特点可以表达如下几种意义：

【一】that从句作“结果状语”：

He was hard-working that he finally succeeded.

他学习勤奋，最后终于成功了。（结果状语）

【二】that从句作“原因状语”：

I am very delighted that you can come.

你能来，我很高兴。（原因状语）

【三】that从句作“目的状语”：

Be careful that you don’t slip on the icy roads. 

小心（目的是）不要在结冰的路上滑倒。（目的状语）

【四】that 从句作“宾语”：

这类形容词，往往带有“认为；相信；确信”等观点类动词的意义，常见的形容词还有：be sure=know, certain, clear, be afraid=fear; be confident=believe等。

The senator is sure that he will get support from the grass roots.

这位参议员相信他能得到基层群众的支持。

I was clear that it should not have been done.

我确信那件事是不应该做的。

She was certain that the young man had gone mad. 

她确信那个年轻人已经发疯。

I am afraid that I can't catch the last bus.

我怕我赶不上最后一趟汽车了。