--- cpp/CMakeLists.txt
+++ cpp/CMakeLists.txt
@@ -109,7 +109,7 @@ set(BUILD_SUPPORT_DIR "${CMAKE_SOURCE_DIR}/build-support")
 set(ARROW_CMAKE_INSTALL_DIR "${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}")
 set(ARROW_DOC_DIR "share/doc/${PROJECT_NAME}")
 
-set(ARROW_LLVM_VERSIONS "10" "9" "8" "7")
+set(ARROW_LLVM_VERSIONS "12" "11" "10" "9" "8" "7")
 list(GET ARROW_LLVM_VERSIONS 0 ARROW_LLVM_VERSION_PRIMARY)
 string(REGEX
        REPLACE "^([0-9]+)(\\..+)?" "\\1" ARROW_LLVM_VERSION_PRIMARY_MAJOR

--- cpp/cmake_modules/ThirdpartyToolchain.cmake
+++ cpp/cmake_modules/ThirdpartyToolchain.cmake
@@ -2092,10 +2092,11 @@ macro(build_re2)
 endmacro()
 
 if(ARROW_GANDIVA)
-  resolve_dependency(RE2)
+  find_package(re2 REQUIRED)
+  resolve_dependency(re2)
 
   # TODO: Don't use global includes but rather target_include_directories
-  get_target_property(RE2_INCLUDE_DIR RE2::re2 INTERFACE_INCLUDE_DIRECTORIES)
+  get_target_property(RE2_INCLUDE_DIR re2::re2 INTERFACE_INCLUDE_DIRECTORIES)
   include_directories(SYSTEM ${RE2_INCLUDE_DIR})
 endif()
 
--- cpp/src/gandiva/CMakeLists.txt
+++ cpp/src/gandiva/CMakeLists.txt
@@ -25,8 +25,14 @@ add_custom_target(gandiva-benchmarks)
 
 add_dependencies(gandiva-all gandiva gandiva-tests gandiva-benchmarks)
 
+# Now LLVMAlt is only for finding clang/llvm-link
 find_package(LLVMAlt REQUIRED)
 
+find_package(llvm-core REQUIRED)
+
+string(REPLACE "." ";" VERSION_LIST ${llvm-core_VERSION})
+list(GET VERSION_LIST 0 LLVM_VERSION_MAJOR)
+
 if(LLVM_VERSION_MAJOR LESS "10")
   set(GANDIVA_CXX_STANDARD ${CMAKE_CXX_STANDARD})
 else()
@@ -88,9 +94,9 @@ set(SRC_FILES
     random_generator_holder.cc
     ${GANDIVA_PRECOMPILED_CC_PATH})
 
-set(GANDIVA_SHARED_PRIVATE_LINK_LIBS arrow_shared LLVM::LLVM_INTERFACE RE2::re2)
+set(GANDIVA_SHARED_PRIVATE_LINK_LIBS arrow_shared llvm-core::llvm-core re2::re2)
 
-set(GANDIVA_STATIC_LINK_LIBS arrow_static LLVM::LLVM_INTERFACE RE2::re2)
+set(GANDIVA_STATIC_LINK_LIBS arrow_static llvm-core::llvm-core re2::re2)
 
 if(ARROW_GANDIVA_STATIC_LIBSTDCPP
    AND (CMAKE_COMPILER_IS_GNUCC OR CMAKE_COMPILER_IS_GNUCXX))
@@ -131,7 +137,7 @@ add_arrow_lib(gandiva
               arrow_dependencies
               precompiled
               EXTRA_INCLUDES
-              $<TARGET_PROPERTY:LLVM::LLVM_INTERFACE,INTERFACE_INCLUDE_DIRECTORIES>
+              $<TARGET_PROPERTY:llvm-core::core,INTERFACE_INCLUDE_DIRECTORIES>
               SHARED_LINK_FLAGS
               ${GANDIVA_SHARED_LINK_FLAGS}
               SHARED_LINK_LIBS
@@ -225,9 +231,9 @@ add_gandiva_test(internals-test
                  decimal_type_util_test.cc
                  random_generator_holder_test.cc
                  EXTRA_DEPENDENCIES
-                 LLVM::LLVM_INTERFACE
+                 llvm-core::llvm-core
                  EXTRA_INCLUDES
-                 $<TARGET_PROPERTY:LLVM::LLVM_INTERFACE,INTERFACE_INCLUDE_DIRECTORIES>
+                 $<TARGET_PROPERTY:llvm-core::core,INTERFACE_INCLUDE_DIRECTORIES>
                  ${GANDIVA_INTERNALS_TEST_ARGUMENTS})
 
 if(ARROW_GANDIVA_JAVA)