没关系,一有消息我就马上告诉你,请问用英语怎么翻译?

看这是在什么情况下用了,楼上的那些答案都不错.
没关系可以用: Don't worry about it, No problem, Relax, Don't sweat it, It's okay...等方法来表达,（基本上可以说,从前往后,最正式到最随意,根据情况 Calm down也可以放在“没关系”的位置）
马上通知的话,I will let you know (inform you) the instant I got the news.
不过一般不这么用,最常用的是“我会尽快通知你” I will inform you ASAP (as soon as possible).
你会是第一个听到的 you would be the first person to know.
想文艺点的话不妨试试: I will deliver the news to you faster than Hermes himself.
P.S. Hermes - 希腊神话里的信使.

Don't worry, I will inform you the moment I got the news.
祝你好运~_~

It doesn't matter, I would inform you once I have got the news.

That's OK. I'll keep you informed.

或者：It doesn't matter, I will let you know as soon as I get any information!

That's OK. Once I get news, I will inform you at the first time.

纯属个人见解。
如果满意，请记得采纳，(*^__^*) 谢谢~~