Your question is not an easy one. Anxiety is not a secondary or auxiliary problem, it's a problem that goes to the very heart of Buddhism and indeed to the very heart of what it means to be alive.
To resolve this problem completely and exhaustively requires complete and perfect penetration into the core principle of Buddhism.
To be perfectly without anxiety is to be perfectly at peace. It's not an easy feat, unless we are taking about sedated "peace" or "peace" of a stupid person unaware of issues. To be perfectly at peace while being fully aware of all the existential trials and tribulations is what we Mahayana Buddhists call to be in Nirvana. This unconditional peace regardless of circumstances requires (is enabled by, depends on, comes from) the special level of insight into the basic principles of sentient existence. We call this level of insight Enlightenment.
I just want to set expectations, so you know what you are asking for, a solution to The Fundamental Problem. It's not something you can achieve "by the way", between other things. It takes extraordinary focus and determination.
The principles themselves are simple, I will explain them to you right now. It is fully grasping the implications and integrating them in one's life is what most people find difficult.
Sentient existence is a phenomenon that is 100% subjective. Everything we ever encounter in life is subsumed in our subjective experience. This subjective experience is a flow of shapes our mind takes. In other words, our entire existence is a sequence of mindstates. I'm not saying nothing else exists, I'm saying mindstates is what really matters because nothing in our actual subjective lives can be experienced outside of mindstates.
Mind is an interpreter. Everything we experience has a meaning to us, pointing to some other meanings, each of them pointing to yet other meanings. We follow these chains of meanings leading us to some conclusions and determinations. We follow associations, memories, stereotypes, generalizations, and signs. Our mindstates, the shapes our subjective existence takes, and our very universe (as we see it) are largely defined by these chains of interpretations.
Our categories of "good" and "bad" are right there among these meanings and signs. Our feeling joyful or fearful or satisfied etc. - is nothing but a step in a series of mindstates induced by the interpretation sequences. When we take some of these meanings and categories very seriously, when we identify with them, when we are attached to them - they lead us down certain interpretation chains that end up feeling bad.
I won't tell you that all our interpretations and all our categories are arbitrary and therefore should be abandoned, no. Although that is not far from the truth, it's technically not accurate. Instead I will say this: our categories and understandings are simplistic and superficial. Being simplistic and superficial they are one-sided and unnecessarily polarized. Being onesided and polarized they lead to conflict (whether tangible or abstract). Anticipation of conflict is anxiety.
Are you with me so far? Anxiety, just like most other discordant mindstates, comes from a clash of interpretations, which comes from attachment to simplistic superficial categories, meanings and signs we have internalized as "the reality". The good news is, it's not the actual reality. The Actual reality is open, multidimensional, and ambiguous in the good sense of the word.
The way to living without anxiety is to let go of the illusory safety and illusory stability of our categories and meanings and values - and to embrace the seeming groundlessness of the truly open mind. This requires undoing one's habitual stereotypes and prejudices not only about life, society, the world - but also about ourselves. When all of these are perfectly open, the process of interpretation has no ground to stand on, leading to indescribable mind no longer terrorized by its content.
To master this Liberation and to get fully confident operating from the perspective of groundlessness, being confidently nobody, undefined - is the only mathematically possible way to absolute and total cessation of anxiety.
In practice the end state looks surprisingly warm and humane. After all, we are born undefined and we die undefined, it's only in the middle that we pretend to be someone we are not. Coming back to being honestly and 100% authentically what you really are feels like putting down an unbearable unnecessary load. Who knew you can simply be your imperfect self and that in itself is the greatest thing in the world and the true Nirvana? It's the simplest thing in the universe but the hardest to grok and master.