diff --git a/docs/middleware/request/authentication.md b/docs/middleware/request/authentication.md
index 3342f1fb5..867289dc2 100644
--- a/docs/middleware/request/authentication.md
+++ b/docs/middleware/request/authentication.md
@@ -23,6 +23,16 @@ Faraday.new(...) do |conn|
 end
 ```
 
+### With a proc
+
+You can also provide a proc, which will be evaluated on each request:
+
+ ```ruby
+ Faraday.new(...) do |conn|
+  conn.request :authorization, 'Bearer', -> { MyAuthStorage.get_auth_token }
+ end
+ ```
+
 ### Basic Authentication
 
 `BasicAuthentication` adds a 'Basic' type Authorization header to a Faraday request.
diff --git a/lib/faraday/request/authorization.rb b/lib/faraday/request/authorization.rb
index f9b56c871..8af00d7f7 100644
--- a/lib/faraday/request/authorization.rb
+++ b/lib/faraday/request/authorization.rb
@@ -1,5 +1,7 @@
 # frozen_string_literal: true
 
+require 'base64'
+
 module Faraday
   class Request
     # Request middleware for the Authorization HTTP header
@@ -39,16 +41,47 @@ def self.build_hash(type, hash)
 
       # @param app [#call]
       # @param type [String, Symbol] Type of Authorization
-      # @param token [String, Symbol, Hash] Token value for the Authorization
-      def initialize(app, type, token)
-        @header_value = self.class.header(type, token)
+      # @param params [Array<String, Proc>] parameters to build the Authorization header.
+      #   If the type is `:basic`, then these can be a login and password pair.
+      #   Otherwise, a single value is expected that will be appended after the type.
+      #   This value can be a proc, in which case it will be invoked on each request.
+      def initialize(app, type, *params)
+        @type = type
+        @params = params
+        @header_value = self.class.header(type, params[0]) unless params[0].is_a? Proc
         super(app)
       end
 
       # @param env [Faraday::Env]
-      def call(env)
-        env.request_headers[KEY] = @header_value unless env.request_headers[KEY]
-        @app.call(env)
+      def on_request(env)
+        return if env.request_headers[KEY]
+
+        env.request_headers[KEY] = header_from(@type, *@params)
+      end
+
+      private
+
+      # @param type [String, Symbol]
+      # @param params [Array]
+      # @return [String] a header value
+      def header_from(type, *params)
+        return @header_value if @header_value
+
+        if type.to_s.casecmp('basic').zero? && params.size == 2
+          basic_header_from(*params)
+        elsif params.size != 1
+          raise ArgumentError, "Unexpected params received (got #{params.size} instead of 1)"
+        else
+          value = params.first
+          value = value.call if value.is_a?(Proc)
+          "#{type} #{value}"
+        end
+      end
+
+      def basic_header_from(login, pass)
+        value = Base64.encode64("#{login}:#{pass}")
+        value.delete!("\n")
+        "Basic #{value}"
       end
     end
   end
diff --git a/spec/faraday/request/authorization_spec.rb b/spec/faraday/request/authorization_spec.rb
index 3f13392e6..9bc23f03d 100644
--- a/spec/faraday/request/authorization_spec.rb
+++ b/spec/faraday/request/authorization_spec.rb
@@ -84,5 +84,13 @@
 
       include_examples 'does not interfere with existing authentication'
     end
+
+    context 'when passed a string and a proc' do
+      let(:auth_config) { ['Bearer', -> { 'custom_from_proc' }] }
+
+      it { expect(response.body).to eq('Bearer custom_from_proc') }
+
+      include_examples 'does not interfere with existing authentication'
+    end
   end
 end